149:@0.938423:0.974518:0.967620:0.974518:0.967620:0.956590:0.938423:0.956590:0.000000:0.000000:0.000000 Pensamiento numérico y variacional :@0.603816:0.043660:0.930949:0.043660:0.930949:0.024915:0.603816:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.193573:0.136836:0.215680:0.136836:0.215680:0.120430:0.193573:0.120430:0.000000:0.000000:0.000000 2:@0.215628:0.140009:0.220865:0.140009:0.220865:0.130428:0.215628:0.130428:0.000000 (9 + 7) = :@0.220818:0.136836:0.312618:0.136836:0.312618:0.120402:0.220818:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.234518:0.130772:0.238864:0.130772:0.238864:0.121208:0.234518:0.121208:0.000000 –1:@0.238821:0.130772:0.249381:0.130772:0.249381:0.121191:0.238821:0.121191:0.000000:0.000000 log:@0.312471:0.136836:0.334578:0.136836:0.334578:0.120430:0.312471:0.120430:0.000000:0.000000:0.000000 2:@0.334521:0.140009:0.339758:0.140009:0.339758:0.130428:0.334521:0.130428:0.000000 (4) + :@0.339710:0.136836:0.377114:0.136836:0.377114:0.120402:0.339710:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.377003:0.136836:0.399110:0.136836:0.399110:0.120430:0.377003:0.120430:0.000000:0.000000:0.000000 2:@0.399053:0.140009:0.404290:0.140009:0.404290:0.130428:0.399053:0.130428:0.000000 (3 + 1):@0.404244:0.136836:0.465358:0.136836:0.465358:0.120402:0.404244:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.417943:0.130772:0.422289:0.130772:0.422289:0.121208:0.417943:0.121208:0.000000 –1:@0.422246:0.130772:0.432806:0.130772:0.432806:0.121191:0.422246:0.121191:0.000000:0.000000 log:@0.193573:0.164199:0.215680:0.164199:0.215680:0.147793:0.193573:0.147793:0.000000:0.000000:0.000000 2:@0.215628:0.167372:0.220865:0.167372:0.220865:0.157791:0.215628:0.157791:0.000000 (9 + 7) :@0.220818:0.164199:0.297763:0.164199:0.297763:0.147766:0.220818:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.234518:0.158135:0.238864:0.158135:0.238864:0.148571:0.234518:0.148571:0.000000 –1:@0.238821:0.158135:0.249381:0.158135:0.249381:0.148555:0.238821:0.148555:0.000000:0.000000 = log:@0.297634:0.164199:0.333878:0.164199:0.333878:0.147793:0.297634:0.147793:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.333831:0.167372:0.339068:0.167372:0.339068:0.157791:0.333831:0.157791:0.000000 (4(3 + 1)),:@0.339022:0.164199:0.421770:0.164199:0.421770:0.147766:0.339022:0.147766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.366421:0.158135:0.370767:0.158135:0.370767:0.148571:0.366421:0.148571:0.000000 –1:@0.370724:0.158135:0.381284:0.158135:0.381284:0.148555:0.370724:0.148555:0.000000:0.000000 log:@0.193573:0.191563:0.215680:0.191563:0.215680:0.175157:0.193573:0.175157:0.000000:0.000000:0.000000 2:@0.215628:0.194735:0.220865:0.194735:0.220865:0.185154:0.215628:0.185154:0.000000 (3:@0.220818:0.191563:0.234605:0.191563:0.234605:0.175129:0.220818:0.175129:0.000000:0.000000 2( –1):@0.234518:0.185499:0.260166:0.185499:0.260166:0.175918:0.234518:0.175918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.242502:0.185499:0.246848:0.185499:0.246848:0.175934:0.242502:0.175934:0.000000 + 7) = :@0.260117:0.191563:0.311529:0.191563:0.311529:0.175129:0.260117:0.175129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.311400:0.191563:0.333507:0.191563:0.333507:0.175157:0.311400:0.175157:0.000000:0.000000:0.000000 2:@0.333453:0.194735:0.338690:0.194735:0.338690:0.185154:0.333453:0.185154:0.000000 (4(3 + 1)).:@0.338642:0.191563:0.421390:0.191563:0.421390:0.175129:0.338642:0.175129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.366041:0.185499:0.370387:0.185499:0.370387:0.175934:0.366041:0.175934:0.000000 –1:@0.370344:0.185499:0.380904:0.185499:0.380904:0.175918:0.370344:0.175918:0.000000:0.000000 La función :@0.103202:0.218925:0.183421:0.218925:0.183421:0.202491:0.103202:0.202491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Log:@0.183384:0.218925:0.208701:0.218925:0.208701:0.202519:0.183384:0.202519:0.000000:0.000000:0.000000 2:@0.208649:0.222098:0.213886:0.222098:0.213886:0.212517:0.208649:0.212517:0.000000 es inyectiva. Aplicando esta propiedad a la ecuación precedente, se :@0.213838:0.218926:0.710788:0.218926:0.710788:0.202492:0.213838:0.202492:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tiene la siguiente ecuación::@0.103210:0.235568:0.300658:0.235568:0.300658:0.219134:0.103210:0.219134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.248039:0.262930:0.257021:0.262930:0.257021:0.246496:0.248039:0.246496:0.000000 2( –1):@0.256934:0.256867:0.282582:0.256867:0.282582:0.247286:0.256934:0.247286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.264919:0.256867:0.269265:0.256867:0.269265:0.247302:0.264919:0.247302:0.000000 + 7 = 4(3 + 1) :@0.282534:0.262931:0.402994:0.262931:0.402994:0.246497:0.282534:0.246497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.351621:0.256867:0.355968:0.256867:0.355968:0.247302:0.351621:0.247302:0.000000 –1:@0.355925:0.256867:0.366484:0.256867:0.366484:0.247286:0.355925:0.247286:0.000000:0.000000 ⇔:@0.402884:0.262515:0.422064:0.262515:0.422064:0.245526:0.402884:0.245526:0.000000 3:@0.421972:0.262931:0.434912:0.262931:0.434912:0.246497:0.421972:0.246497:0.000000:0.000000 2( –1):@0.434819:0.256867:0.460467:0.256867:0.460467:0.247286:0.434819:0.247286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.442803:0.256867:0.447149:0.256867:0.447149:0.247302:0.442803:0.247302:0.000000 + 3 = 4 × 3 .:@0.460418:0.262931:0.561517:0.262931:0.561517:0.246497:0.460418:0.246497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.543498:0.256867:0.547845:0.256867:0.547845:0.247302:0.543498:0.247302:0.000000 –1:@0.547802:0.256867:0.558361:0.256867:0.558361:0.247286:0.547802:0.247286:0.000000:0.000000 La solución de esta última ecuación no se obtiene de inmediato. La transformamos :@0.103214:0.290293:0.710843:0.290293:0.710843:0.273859:0.103214:0.273859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en una ecuación de segundo grado. Para el efecto, ponemos = 3 . Entonces, = :@0.103214:0.306935:0.710373:0.306936:0.710373:0.290502:0.103214:0.290501:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.547049:0.306935:0.554780:0.306935:0.554780:0.290529:0.547049:0.290529:0.000000 x:@0.582554:0.300872:0.586900:0.300872:0.586900:0.291307:0.582554:0.291307:0.000000 –1:@0.586857:0.300872:0.597417:0.300872:0.597417:0.291291:0.586857:0.291291:0.000000:0.000000 v:@0.678491:0.306936:0.686222:0.306936:0.686222:0.290530:0.678491:0.290530:0.000000 2:@0.686158:0.300872:0.691395:0.300872:0.691395:0.291291:0.686158:0.291291:0.000000 (3 ) = 3:@0.103219:0.323578:0.169508:0.323578:0.169508:0.307144:0.103219:0.307144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.116909:0.317514:0.121255:0.317514:0.121255:0.307949:0.116909:0.307949:0.000000 –1 2:@0.121212:0.317514:0.141759:0.316253:0.141759:0.306672:0.121212:0.307933:0.000000:0.000000:0.000000:0.000000 2( –1):@0.169406:0.317514:0.195054:0.317514:0.195054:0.307933:0.169406:0.307933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.177390:0.317514:0.181736:0.317514:0.181736:0.307949:0.177390:0.307949:0.000000 . Obtenemos la ecuación + 3 = 4 . Así,:@0.195006:0.323578:0.486477:0.323578:0.486477:0.307144:0.195006:0.307144:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.379189:0.323578:0.386920:0.323578:0.386920:0.307172:0.379189:0.307172:0.000000 2:@0.386848:0.317514:0.392085:0.317514:0.392085:0.307933:0.386848:0.307933:0.000000 v:@0.447424:0.323578:0.455155:0.323578:0.455155:0.307172:0.447424:0.307172:0.000000 v:@0.103209:0.350940:0.110940:0.350940:0.110940:0.334534:0.103209:0.334534:0.000000 2:@0.110875:0.344877:0.116111:0.344877:0.116111:0.335296:0.110875:0.335296:0.000000 + 3 = 4 :@0.116065:0.350941:0.183141:0.350941:0.183141:0.334507:0.116065:0.334507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.171452:0.350941:0.179183:0.350941:0.179183:0.334535:0.171452:0.334535:0.000000 ⇔:@0.183067:0.350525:0.202247:0.350525:0.202247:0.333536:0.183067:0.333536:0.000000 – 4 + 3 = 0 :@0.202155:0.350941:0.312009:0.350941:0.312009:0.334507:0.202155:0.334507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.206113:0.350941:0.213844:0.350941:0.213844:0.334535:0.206113:0.334535:0.000000 2:@0.213771:0.344877:0.219008:0.344877:0.219008:0.335296:0.213771:0.335296:0.000000 v:@0.244878:0.350941:0.252609:0.350941:0.252609:0.334535:0.244878:0.334535:0.000000 ⇔:@0.311880:0.350525:0.331060:0.350525:0.331060:0.333536:0.311880:0.333536:0.000000 ( – 3)( – 1) = 0 :@0.103197:0.378303:0.221353:0.378303:0.221353:0.361869:0.103197:0.361869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.108001:0.378303:0.115732:0.378303:0.115732:0.361897:0.108001:0.361897:0.000000 v:@0.151185:0.378303:0.158916:0.378303:0.158916:0.361897:0.151185:0.361897:0.000000 ⇔ :@0.221206:0.377887:0.244896:0.377887:0.244896:0.360898:0.221206:0.360898:0.000000:0.000000 :@0.244804:0.378303:0.351732:0.378303:0.351732:0.361869:0.244804:0.361869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.351474:0.377887:0.370654:0.377887:0.370654:0.360898:0.351474:0.360898:0.000000 Para – 3, resulta 3 = 3 :@0.103197:0.405665:0.289857:0.405667:0.289857:0.389234:0.103197:0.389231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.141613:0.405665:0.149344:0.405665:0.149344:0.389259:0.141613:0.389259:0.000000 x:@0.271009:0.399604:0.275355:0.399604:0.275355:0.390039:0.271009:0.390039:0.000000 –1:@0.275312:0.399604:0.285872:0.399604:0.285872:0.390023:0.275312:0.390023:0.000000:0.000000 ⇔:@0.289783:0.405251:0.308963:0.405251:0.308963:0.388263:0.289783:0.388263:0.000000 – 1 = 1 :@0.308871:0.405667:0.377917:0.405667:0.377917:0.389234:0.308871:0.389234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.312829:0.405667:0.320284:0.405667:0.320284:0.389261:0.312829:0.389261:0.000000 ⇔:@0.377788:0.405251:0.396968:0.405251:0.396968:0.388263:0.377788:0.388263:0.000000 = 2.:@0.396876:0.405667:0.439139:0.405667:0.439139:0.389234:0.396876:0.389234:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.400834:0.405667:0.408289:0.405667:0.408289:0.389261:0.400834:0.389261:0.000000 Para – 1, se obtiene 1 = 3 :@0.103225:0.433029:0.313955:0.433029:0.313955:0.416596:0.103225:0.416596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.137684:0.433029:0.145415:0.433029:0.145415:0.416623:0.137684:0.416623:0.000000 x:@0.295108:0.426965:0.299454:0.426965:0.299454:0.417401:0.295108:0.417401:0.000000 –1:@0.299411:0.426965:0.309971:0.426965:0.309971:0.417385:0.299411:0.417385:0.000000:0.000000 ⇔:@0.313881:0.432613:0.333062:0.432613:0.333062:0.415625:0.313881:0.415625:0.000000 – 1 = 0 :@0.332970:0.433029:0.402015:0.433029:0.402015:0.416596:0.332970:0.416596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.336927:0.433029:0.344382:0.433029:0.344382:0.416623:0.336927:0.416623:0.000000 ⇔:@0.401886:0.432613:0.421067:0.432613:0.421067:0.415625:0.401886:0.415625:0.000000 = 1.:@0.420975:0.433029:0.463238:0.433029:0.463238:0.416596:0.420975:0.416596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.424932:0.433029:0.432387:0.433029:0.432387:0.416623:0.424932:0.416623:0.000000 Las soluciones son = 1 y = 2. Verifiquemos que = 2 es solución. Calculemos el :@0.103229:0.460391:0.710410:0.460391:0.710410:0.443957:0.103229:0.443957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.244026:0.460391:0.251481:0.460391:0.251481:0.443985:0.244026:0.443985:0.000000 x:@0.297131:0.460391:0.304586:0.460391:0.304586:0.443985:0.297131:0.443985:0.000000 x:@0.473822:0.460391:0.481277:0.460391:0.481277:0.443985:0.473822:0.443985:0.000000 primer miembro de la ecuación::@0.103247:0.477033:0.335716:0.477033:0.335716:0.460599:0.103247:0.460599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103247:0.504395:0.110720:0.504395:0.110720:0.487989:0.103247:0.487989:0.000000 = :@0.110647:0.504395:0.129533:0.504395:0.129533:0.487961:0.110647:0.487961:0.000000:0.000000:0.000000 log:@0.129441:0.504395:0.151548:0.504395:0.151548:0.487989:0.129441:0.487989:0.000000:0.000000:0.000000 2:@0.151462:0.507570:0.156699:0.507570:0.156699:0.497989:0.151462:0.497989:0.000000 (9 + 7) = :@0.156653:0.504398:0.236579:0.504398:0.236579:0.487964:0.156653:0.487964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.170352:0.498334:0.174698:0.498334:0.174698:0.488769:0.170352:0.488769:0.000000 –1:@0.174655:0.498334:0.185215:0.498334:0.185215:0.488753:0.174655:0.488753:0.000000:0.000000 log:@0.236450:0.504398:0.258557:0.504398:0.258557:0.487992:0.236450:0.487992:0.000000:0.000000:0.000000 2:@0.258504:0.507570:0.263741:0.507570:0.263741:0.497989:0.258504:0.497989:0.000000 (9 + 7) = :@0.263695:0.504398:0.344503:0.504398:0.344503:0.487964:0.263695:0.487964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2–1:@0.277393:0.498334:0.293147:0.498334:0.293147:0.488753:0.277393:0.488753:0.000000:0.000000:0.000000 log:@0.344374:0.504398:0.366481:0.504398:0.366481:0.487992:0.344374:0.487992:0.000000:0.000000:0.000000 2:@0.366429:0.507570:0.371666:0.507570:0.371666:0.497989:0.366429:0.497989:0.000000 (16) = 4.:@0.371618:0.504398:0.429969:0.504398:0.429969:0.487964:0.371618:0.487964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Calculemos el segundo miembro::@0.103204:0.531760:0.347768:0.531760:0.347768:0.515326:0.103204:0.515326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.204336:0.559124:0.211810:0.559124:0.211810:0.542718:0.204336:0.542718:0.000000 = 2 + :@0.211736:0.559124:0.258343:0.559124:0.258343:0.542690:0.211736:0.542690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.258214:0.559124:0.280322:0.559124:0.280322:0.542718:0.258214:0.542718:0.000000:0.000000:0.000000 2:@0.280281:0.562296:0.285518:0.562296:0.285518:0.552715:0.280281:0.552715:0.000000 (3 + 1) = 2 + :@0.285472:0.559124:0.393120:0.559124:0.393120:0.542690:0.285472:0.542690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.299171:0.553060:0.303517:0.553060:0.303517:0.543495:0.299171:0.543495:0.000000 –1:@0.303474:0.553060:0.314034:0.553060:0.314034:0.543479:0.303474:0.543479:0.000000:0.000000 log:@0.392954:0.559124:0.415061:0.559124:0.415061:0.542718:0.392954:0.542718:0.000000:0.000000:0.000000 2:@0.415016:0.562296:0.420253:0.562296:0.420253:0.552715:0.415016:0.552715:0.000000 (3 + 1) = 2 + :@0.420207:0.559124:0.528736:0.559124:0.528736:0.542690:0.420207:0.542690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2–1:@0.433905:0.553060:0.449659:0.553060:0.449659:0.543479:0.433905:0.543479:0.000000:0.000000:0.000000 log:@0.528570:0.559124:0.550677:0.559124:0.550677:0.542718:0.528570:0.542718:0.000000:0.000000:0.000000 2:@0.550632:0.562296:0.555869:0.562296:0.555869:0.552715:0.550632:0.552715:0.000000 (4) = 4.:@0.555823:0.559124:0.605265:0.559124:0.605265:0.542690:0.555823:0.542690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4. Estudia la existencia de soluciones en y resuelve la ecuación:@0.073089:0.586487:0.571835:0.586487:0.571835:0.569818:0.073089:0.569818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ℝ:@0.389466:0.587070:0.402756:0.587070:0.402756:0.569415:0.389466:0.569415:0.000000 log x:@0.305326:0.611353:0.344831:0.611349:0.344831:0.594943:0.305326:0.594947:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.327382:0.614521:0.332619:0.614521:0.332619:0.604941:0.327382:0.604941:0.000000 ( + 2) – :@0.332571:0.611349:0.394401:0.611349:0.394401:0.594915:0.332571:0.594915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.394272:0.611349:0.416380:0.611349:0.416380:0.594943:0.394272:0.594943:0.000000:0.000000:0.000000 2:@0.416328:0.614521:0.421565:0.614521:0.421565:0.604941:0.416328:0.604941:0.000000 (2 – 3) = 2.:@0.421517:0.611349:0.504276:0.611349:0.504276:0.594915:0.421517:0.594915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.435212:0.611349:0.442667:0.611349:0.442667:0.594943:0.435212:0.594943:0.000000 Primeramente, la función :@0.103200:0.638711:0.289379:0.638711:0.289379:0.622277:0.103200:0.622277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Log:@0.289150:0.638711:0.314468:0.638711:0.314468:0.622305:0.289150:0.622305:0.000000:0.000000:0.000000 2:@0.314425:0.641885:0.319662:0.641885:0.319662:0.632304:0.314425:0.632304:0.000000 tiene como dominio el conjunto ]0, ∞[.:@0.319614:0.638712:0.605306:0.638712:0.605306:0.622279:0.319614:0.622279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego, :@0.103219:0.658932:0.156108:0.658932:0.156108:0.642498:0.103219:0.642498:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log x:@0.155992:0.658932:0.195494:0.658927:0.195494:0.642521:0.155992:0.642526:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.178044:0.662099:0.183281:0.662099:0.183281:0.652519:0.178044:0.652519:0.000000 ( + 2) está bien definido, si y solo si,:@0.183235:0.658927:0.443453:0.658927:0.443453:0.642493:0.183235:0.642493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.336181:0.686289:0.343636:0.686289:0.343636:0.669883:0.336181:0.669883:0.000000 + 2 > 0 :@0.343562:0.686289:0.403036:0.686289:0.403036:0.669855:0.343562:0.669855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.402907:0.685873:0.422088:0.685873:0.422088:0.668884:0.402907:0.668884:0.000000 > –2.:@0.421995:0.686289:0.473389:0.686289:0.473389:0.669855:0.421995:0.669855:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.425953:0.686289:0.433408:0.686289:0.433408:0.669883:0.425953:0.669883:0.000000 De manera similar, :@0.103200:0.713651:0.240616:0.713651:0.240616:0.697217:0.103200:0.697217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.240426:0.713651:0.262533:0.713651:0.262533:0.697245:0.240426:0.697245:0.000000:0.000000:0.000000 2:@0.262485:0.716826:0.267722:0.716826:0.267722:0.707245:0.262485:0.707245:0.000000 (2 – 3) está bien definido, si y solo si,:@0.267674:0.713654:0.535016:0.713654:0.535016:0.697220:0.267674:0.697220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.281369:0.713654:0.288824:0.713654:0.288824:0.697247:0.281369:0.697247:0.000000 2 – 3 > 0 :@0.103205:0.745023:0.177202:0.745023:0.177202:0.728590:0.103205:0.728590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.112114:0.745023:0.119569:0.745023:0.119569:0.728617:0.112114:0.728617:0.000000 ⇔:@0.177074:0.744607:0.196254:0.744607:0.196254:0.727619:0.177074:0.727619:0.000000 > De estos dos resultados,:@0.196162:0.745023:0.421143:0.745025:0.421143:0.728591:0.196162:0.728590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.200119:0.745023:0.207574:0.745023:0.207574:0.728617:0.200119:0.728617:0.000000 3:@0.224489:0.737550:0.233472:0.737550:0.233472:0.721116:0.224489:0.721116:0.000000 2:@0.224489:0.753942:0.233472:0.753942:0.233472:0.737508:0.224489:0.737508:0.000000 .:@0.239491:0.745025:0.242823:0.745025:0.242823:0.728619:0.239491:0.728619:0.000000 log x:@0.103204:0.768809:0.142714:0.768809:0.142714:0.752403:0.103204:0.752403:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.125265:0.771981:0.130502:0.771981:0.130502:0.762400:0.125265:0.762400:0.000000 ( + 2) – :@0.130455:0.768809:0.192285:0.768809:0.192285:0.752375:0.130455:0.752375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.192156:0.768809:0.214263:0.768809:0.214263:0.752403:0.192156:0.752403:0.000000:0.000000:0.000000 2:@0.214211:0.771981:0.219448:0.771981:0.219448:0.762400:0.214211:0.762400:0.000000 (2 – 3) está bien definido, si y solo si:@0.219400:0.768809:0.483612:0.768809:0.483612:0.752375:0.219400:0.752375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.233095:0.768809:0.240550:0.768809:0.240550:0.752403:0.233095:0.752403:0.000000 x:@0.103195:0.800178:0.110650:0.800178:0.110650:0.783772:0.103195:0.783772:0.000000 > –2 y > , de donde > . Observa la Figura 4.9.:@0.110577:0.800178:0.500994:0.800180:0.500994:0.783746:0.110577:0.783745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.171210:0.800178:0.178665:0.800178:0.178665:0.783772:0.171210:0.783772:0.000000 3:@0.199564:0.792705:0.208547:0.792705:0.208547:0.776271:0.199564:0.776271:0.000000 2:@0.199564:0.809097:0.208547:0.809097:0.208547:0.792663:0.199564:0.792663:0.000000 x:@0.296791:0.800180:0.304246:0.800180:0.304246:0.783774:0.296791:0.783774:0.000000 3:@0.325133:0.792705:0.334116:0.792705:0.334116:0.776271:0.325133:0.776271:0.000000 2:@0.325133:0.809097:0.334116:0.809097:0.334116:0.792663:0.325133:0.792663:0.000000 Si la ecuación tiene solución , esta debe satisfacer:@0.103197:0.827542:0.468231:0.827542:0.468231:0.811108:0.103197:0.811108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.311862:0.827542:0.319316:0.827542:0.319316:0.811136:0.311862:0.811136:0.000000 la condición > . Resolvamos la ecuación. Tenemos:@0.103179:0.859799:0.492237:0.859797:0.492237:0.843363:0.103179:0.843365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.195896:0.859799:0.203351:0.859799:0.203351:0.843393:0.195896:0.843393:0.000000 3:@0.224256:0.851434:0.233239:0.851434:0.233239:0.835000:0.224256:0.835000:0.000000 2:@0.224256:0.867826:0.233239:0.867826:0.233239:0.851392:0.224256:0.851392:0.000000 log x:@0.103210:0.883581:0.142715:0.883586:0.142715:0.867180:0.103210:0.867174:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.125265:0.886758:0.130502:0.886758:0.130502:0.877177:0.125265:0.877177:0.000000 ( + 2) – :@0.130455:0.883586:0.192285:0.883586:0.192285:0.867152:0.130455:0.867152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 log:@0.192157:0.883586:0.214264:0.883586:0.214264:0.867180:0.192157:0.867180:0.000000:0.000000:0.000000 2:@0.214211:0.886758:0.219448:0.886758:0.219448:0.877177:0.214211:0.877177:0.000000 (2 – 3) = 2 :@0.219402:0.883586:0.302989:0.883586:0.302989:0.867152:0.219402:0.867152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.233097:0.883586:0.240552:0.883586:0.240552:0.867180:0.233097:0.867180:0.000000 ⇔:@0.302842:0.883170:0.322022:0.883170:0.322022:0.866181:0.302842:0.866181:0.000000 :@0.321930:0.883586:0.325962:0.883586:0.325962:0.867152:0.321930:0.867152:0.000000 log:@0.325888:0.883586:0.347995:0.883586:0.347995:0.867180:0.325888:0.867180:0.000000:0.000000:0.000000 2:@0.347951:0.886758:0.353188:0.886758:0.353188:0.877177:0.347951:0.877177:0.000000 = 2 :@0.353142:0.883586:0.444258:0.883586:0.444258:0.867152:0.353142:0.867152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.444037:0.883170:0.463218:0.883170:0.463218:0.866181:0.444037:0.866181:0.000000 = 2:@0.463126:0.883586:0.542369:0.883586:0.542369:0.867152:0.463126:0.867152:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.542183:0.877522:0.547420:0.877522:0.547420:0.867941:0.542183:0.867941:0.000000 ⇔:@0.103210:0.906960:0.122390:0.906960:0.122390:0.889971:0.103210:0.889971:0.000000 + 2 = 8x – 12 :@0.122298:0.907376:0.235098:0.907376:0.235098:0.890942:0.122298:0.890942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.126256:0.907376:0.136950:0.907376:0.136950:0.890970:0.126256:0.890970:0.000000:0.000000 ⇔:@0.234932:0.906960:0.254112:0.906960:0.254112:0.889971:0.234932:0.889971:0.000000 7x = 14 :@0.254020:0.907376:0.315372:0.907376:0.315372:0.890942:0.254020:0.890942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⇔:@0.315243:0.906960:0.334423:0.906960:0.334423:0.889971:0.315243:0.889971:0.000000 = 2.:@0.334331:0.907376:0.376594:0.907376:0.376594:0.890942:0.334331:0.890942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.338289:0.907376:0.345744:0.907376:0.345744:0.890970:0.338289:0.890970:0.000000 Así, la solución es = 2. Nota que esta satisface la condición > .:@0.103228:0.938745:0.595855:0.938747:0.595855:0.922313:0.103228:0.922312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.232374:0.938745:0.239828:0.938745:0.239828:0.922339:0.232374:0.922339:0.000000 x:@0.537455:0.938745:0.544910:0.938745:0.544910:0.922339:0.537455:0.922339:0.000000 3:@0.569735:0.931272:0.578718:0.931272:0.578718:0.914838:0.569735:0.914838:0.000000 2:@0.569735:0.947664:0.578718:0.947664:0.578718:0.931230:0.569735:0.931230:0.000000 v:@0.252505:0.371274:0.260236:0.371274:0.260236:0.354868:0.252505:0.354868:0.000000 – 3 = 0, o:@0.260236:0.371274:0.335558:0.371274:0.335558:0.354840:0.260236:0.354840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.252505:0.387916:0.260236:0.387916:0.260236:0.371510:0.252505:0.371510:0.000000 – 1 = 0:@0.260236:0.387916:0.314500:0.387916:0.314500:0.371482:0.260236:0.371482:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.386381:0.371274:0.394112:0.371274:0.394112:0.354868:0.386381:0.354868:0.000000 = 3, o:@0.394112:0.371274:0.443186:0.371274:0.443186:0.354840:0.394112:0.354840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.386381:0.387916:0.394112:0.387916:0.394112:0.371510:0.386381:0.371510:0.000000 = 1.:@0.394112:0.387916:0.425331:0.387916:0.425331:0.371482:0.394112:0.371482:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.366555:0.882387:0.374009:0.882387:0.374009:0.865981:0.366555:0.865981:0.000000 + 2:@0.374009:0.882387:0.402025:0.882387:0.402025:0.865953:0.374009:0.865953:0.000000:0.000000:0.000000:0.000000 2 – 3:@0.362947:0.898779:0.405633:0.898779:0.405633:0.882345:0.362947:0.882345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.371929:0.898779:0.379384:0.898779:0.379384:0.882373:0.371929:0.882373:0.000000 x:@0.472470:0.882387:0.479925:0.882387:0.479925:0.865981:0.472470:0.865981:0.000000 + 2:@0.479925:0.882387:0.507941:0.882387:0.507941:0.865953:0.479925:0.865953:0.000000:0.000000:0.000000:0.000000 2 – 3:@0.468862:0.898779:0.511548:0.898779:0.511548:0.882345:0.468862:0.882345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.477845:0.898779:0.485300:0.898779:0.485300:0.882373:0.477845:0.882373:0.000000 p:@0.735054:0.894545:0.746522:0.894545:0.746522:0.884493:0.735054:0.884493:0.000000 :@0.746522:0.895204:0.749454:0.895204:0.749454:0.883253:0.746522:0.883253:0.000000 Figura 4.9.:@0.749454:0.895204:0.803109:0.895204:0.803109:0.883253:0.749454:0.883253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.776750:0.803661:0.782466:0.803661:0.782466:0.793203:0.776750:0.793203:0.000000 x:@0.950259:0.807587:0.955680:0.807587:0.955680:0.795655:0.950259:0.795655:0.000000 1:@0.801513:0.806752:0.807229:0.806752:0.807229:0.796294:0.801513:0.796294:0.000000 –1:@0.761827:0.806752:0.773400:0.806752:0.773400:0.796294:0.761827:0.796294:0.000000:0.000000 –2:@0.742851:0.806752:0.754424:0.806752:0.754424:0.796294:0.742851:0.796294:0.000000:0.000000 2:@0.820489:0.806752:0.826205:0.806752:0.826205:0.796294:0.820489:0.796294:0.000000 3:@0.839465:0.806752:0.845182:0.806752:0.845182:0.796294:0.839465:0.796294:0.000000 3,5:@0.849807:0.801013:0.859429:0.801013:0.859429:0.793543:0.849807:0.793543:0.000000:0.000000:0.000000 5,5:@0.886011:0.801013:0.895633:0.801013:0.895633:0.793543:0.886011:0.793543:0.000000:0.000000:0.000000 4:@0.858435:0.806752:0.864151:0.806752:0.864151:0.796294:0.858435:0.796294:0.000000 5:@0.877411:0.806752:0.883127:0.806752:0.883127:0.796294:0.877411:0.796294:0.000000 6:@0.896387:0.806752:0.902104:0.806752:0.902104:0.796294:0.896387:0.796294:0.000000 7:@0.915363:0.806752:0.921080:0.806752:0.921080:0.796294:0.915363:0.796294:0.000000 8:@0.934340:0.806752:0.940056:0.806752:0.940056:0.796294:0.934340:0.796294:0.000000 1:@0.773628:0.783806:0.779344:0.783806:0.779344:0.773349:0.773628:0.773349:0.000000 –1:@0.767771:0.812400:0.779344:0.812400:0.779344:0.801942:0.767771:0.801942:0.000000:0.000000 –2:@0.767771:0.826697:0.779344:0.826697:0.779344:0.816239:0.767771:0.816239:0.000000:0.000000 –3:@0.767771:0.840994:0.779344:0.840994:0.779344:0.830536:0.767771:0.830536:0.000000:0.000000 2:@0.773628:0.769518:0.779344:0.769518:0.779344:0.759061:0.773628:0.759061:0.000000 3:@0.773628:0.755222:0.779344:0.755222:0.779344:0.744764:0.773628:0.744764:0.000000 y:@0.773193:0.729720:0.778628:0.729720:0.778628:0.717789:0.773193:0.717789:0.000000 y:@0.818702:0.747742:0.824137:0.747742:0.824137:0.735810:0.818702:0.735810:0.000000 = :@0.824137:0.747742:0.837979:0.747742:0.837979:0.735790:0.824137:0.735790:0.000000:0.000000:0.000000 log x:@0.837979:0.747742:0.866942:0.747742:0.866942:0.735810:0.837979:0.735810:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.854164:0.750049:0.857973:0.750049:0.857973:0.743081:0.854164:0.743081:0.000000 ( +2):@0.857973:0.747742:0.885002:0.747742:0.885002:0.735790:0.857973:0.735790:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.855229:0.775125:0.860664:0.775125:0.860664:0.763193:0.855229:0.763193:0.000000 = :@0.860664:0.775125:0.874506:0.775125:0.874506:0.763173:0.860664:0.763173:0.000000:0.000000:0.000000 log:@0.874506:0.775125:0.890691:0.775125:0.890691:0.763193:0.874506:0.763193:0.000000:0.000000:0.000000 2:@0.890689:0.777430:0.894498:0.777430:0.894498:0.770462:0.890689:0.770462:0.000000 (2 –3):@0.894498:0.775122:0.926774:0.775122:0.926774:0.763171:0.894498:0.763171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.904578:0.775122:0.910000:0.775122:0.910000:0.763191:0.904578:0.763191:0.000000 asíntota:@0.745965:0.863295:0.783097:0.863295:0.783097:0.852837:0.745965:0.852837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 asíntota:@0.807239:0.862624:0.844372:0.862624:0.844372:0.852167:0.807239:0.852167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.752384:0.872120:0.757128:0.872120:0.757128:0.861680:0.752384:0.861680:0.000000 = –2:@0.757128:0.872120:0.780813:0.872120:0.780813:0.861662:0.757128:0.861662:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.808352:0.875906:0.813096:0.875906:0.813096:0.865466:0.808352:0.865466:0.000000 = :@0.813096:0.875906:0.825208:0.875906:0.825208:0.865449:0.813096:0.865449:0.000000:0.000000:0.000000 3:@0.825088:0.871411:0.830722:0.871411:0.830722:0.861102:0.825088:0.861102:0.000000 2:@0.825088:0.881241:0.830722:0.881241:0.830722:0.870932:0.825088:0.870932:0.000000 Competencia :@0.740294:0.150262:0.848854:0.150262:0.848854:0.133315:0.740294:0.133315:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.166904:0.837769:0.166904:0.837769:0.149957:0.740294:0.149957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Para resolver ecuaciones :@0.744288:0.186502:0.909065:0.186502:0.909065:0.171562:0.744288:0.171562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 exponenciales, puedes :@0.744288:0.201631:0.898651:0.201631:0.898651:0.186691:0.744288:0.186691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 proceder así::@0.744288:0.216760:0.828018:0.216760:0.828018:0.201820:0.744288:0.201820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Descomponer la :@0.744288:0.231889:0.871633:0.231889:0.871633:0.216949:0.744288:0.216949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 parte numérica en :@0.758519:0.247018:0.884187:0.247018:0.884187:0.232078:0.758519:0.232078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sus factores primos e :@0.758519:0.262147:0.900646:0.262147:0.900646:0.247207:0.758519:0.247207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 igualar bases solo si es :@0.758519:0.277276:0.909592:0.277276:0.909592:0.262336:0.758519:0.262336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 factible.:@0.758519:0.292405:0.809912:0.292405:0.809912:0.277465:0.758519:0.277465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Aplicar logaritmos :@0.744288:0.307534:0.882495:0.307534:0.882495:0.292594:0.744288:0.292594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a los dos lados de la :@0.758519:0.322662:0.893460:0.322662:0.893460:0.307723:0.758519:0.307723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 igualdad (porque la :@0.758519:0.337791:0.891280:0.337791:0.891280:0.322852:0.758519:0.322852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función logarítmica es :@0.758519:0.352920:0.908667:0.352920:0.908667:0.337981:0.758519:0.337981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inyectiva).:@0.758519:0.368049:0.824308:0.368049:0.824308:0.353109:0.758519:0.353109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Efectuar correctamente :@0.744288:0.383178:0.917428:0.383178:0.917428:0.368238:0.744288:0.368238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las operaciones :@0.758519:0.398307:0.864275:0.398307:0.864275:0.383367:0.758519:0.383367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 indicadas.:@0.758519:0.413436:0.823707:0.413436:0.823707:0.398496:0.758519:0.398496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.740294:0.476190:0.848854:0.476190:0.848854:0.459243:0.740294:0.459243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.492832:0.837769:0.492832:0.837769:0.475885:0.740294:0.475885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las matemáticas son un :@0.744288:0.512429:0.906600:0.512429:0.906600:0.497489:0.744288:0.497489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lenguaje universal de la :@0.744288:0.527557:0.902918:0.527557:0.902918:0.512618:0.744288:0.512618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 naturaleza. El ser humano :@0.744288:0.542686:0.917027:0.542686:0.917027:0.527747:0.744288:0.527747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 reconoce e interpreta las :@0.744288:0.557815:0.911081:0.557815:0.911081:0.542876:0.744288:0.542876:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relaciones matemáticas, :@0.744288:0.572944:0.905818:0.572944:0.905818:0.558004:0.744288:0.558004:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pero no las cambia.:@0.744288:0.588073:0.872346:0.588073:0.872346:0.573133:0.744288:0.573133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Escribe:@0.744288:0.611523:0.793598:0.611523:0.793598:0.596369:0.744288:0.596369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tu opinión acerca :@0.793502:0.611523:0.916038:0.611523:0.916038:0.596583:0.793502:0.596583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de esta afirmación.:@0.744288:0.626652:0.868330:0.626652:0.868330:0.611712:0.744288:0.611712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000