18:@0.067867:0.963104:0.095634:0.963104:0.095634:0.941283:0.067867:0.941283:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
El agua pura, ¿qué valor :@0.086291:0.192000:0.247834:0.192000:0.247834:0.177101:0.086291:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de pH tiene?:@0.159499:0.205830:0.244166:0.205830:0.244166:0.190931:0.159499:0.190931:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.068421:0.315785:0.068421:0.272960:0.056510:0.272960:0.056510:0.315785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para graficar funciones :@0.094422:0.450448:0.248427:0.450448:0.248427:0.435549:0.094422:0.435549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logarítmicas, puedes :@0.107137:0.464279:0.248425:0.464279:0.248425:0.449379:0.107137:0.449379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emplear el programa :@0.104658:0.478109:0.248425:0.478109:0.248425:0.463210:0.104658:0.463210:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
GeoGebra :@0.082360:0.491939:0.154061:0.491939:0.154061:0.477040:0.082360:0.477040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
online:@0.154061:0.491939:0.193714:0.491939:0.193714:0.477065:0.154061:0.477065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 clásico. :@0.193714:0.491939:0.248425:0.491939:0.248425:0.477040:0.193714:0.477040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la entrada coloca:@0.110337:0.505769:0.244758:0.505769:0.244758:0.490870:0.110337:0.490870:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función   = log( ), :@0.110856:0.519600:0.248427:0.519600:0.248427:0.504701:0.110856:0.504701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.180479:0.519600:0.187281:0.519600:0.187281:0.504726:0.180479:0.504726:0.000000
x:@0.230619:0.519600:0.237404:0.519600:0.237404:0.504726:0.230619:0.504726:0.000000
puedes ingresar a través :@0.083801:0.533430:0.248425:0.533430:0.248425:0.518531:0.083801:0.518531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del siguiente enlace: :@0.108293:0.547260:0.248425:0.547260:0.248425:0.532361:0.108293:0.532361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/13mtc02:@0.134343:0.564649:0.244757:0.564649:0.244757:0.549524:0.134343:0.549524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Digital:@0.146708:0.417724:0.197179:0.417724:0.197179:0.400824:0.146708:0.400824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función exponencial :@0.287495:0.419061:0.465893:0.419061:0.465893:0.402672:0.287495:0.402672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ya a:@0.471861:0.419011:0.534119:0.419011:0.534119:0.402649:0.471861:0.402649:0.000000:0.000000:0.000000:0.000000
x:@0.507773:0.411350:0.512098:0.411350:0.512098:0.401867:0.507773:0.401867:0.000000
=:@0.484058:0.418596:0.494175:0.418596:0.494175:0.401654:0.484058:0.401654:0.000000
a:@0.576576:0.419011:0.585846:0.419011:0.585846:0.402649:0.576576:0.402649:0.000000
>:@0.537620:0.418596:0.547737:0.418596:0.547737:0.401654:0.537620:0.401654:0.000000
≠:@0.589347:0.418596:0.599464:0.418596:0.599464:0.401654:0.589347:0.401654:0.000000
0 y :@0.550649:0.419011:0.576558:0.419011:0.576558:0.402622:0.550649:0.402622:0.000000:0.000000:0.000000:0.000000
1 es biyectiva, es decir, tiene función in-:@0.601527:0.419011:0.903659:0.419061:0.903659:0.402672:0.601527:0.402622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
versa. Para calcularla, intercambiamos   por  , e   por  ; se obtiene: :@0.287494:0.436957:0.798896:0.436957:0.798896:0.420568:0.287494:0.420568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.574523:0.436957:0.581986:0.436957:0.581986:0.420596:0.574523:0.420596:0.000000
y:@0.619394:0.436957:0.626876:0.436957:0.626876:0.420596:0.619394:0.420596:0.000000
y:@0.651016:0.436957:0.658497:0.436957:0.658497:0.420596:0.651016:0.420596:0.000000
x:@0.695905:0.436957:0.703369:0.436957:0.703369:0.420596:0.695905:0.420596:0.000000
xa:@0.804778:0.436915:0.839551:0.436915:0.839551:0.420553:0.804778:0.420553:0.000000:0.000000
y:@0.840847:0.429252:0.845183:0.429252:0.845183:0.419770:0.840847:0.419770:0.000000
=:@0.816975:0.436500:0.827092:0.436500:0.827092:0.419558:0.816975:0.419558:0.000000
,  o sea, :@0.848280:0.436915:0.907673:0.436956:0.907673:0.420567:0.848280:0.420526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.287490:0.453552:0.294972:0.453552:0.294972:0.437191:0.287490:0.437191:0.000000
 es el exponente al que hay que elevar una base   para obtener  . Si reemplazamos :@0.294972:0.453552:0.907671:0.453552:0.907671:0.437164:0.294972:0.437164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.651359:0.453552:0.660628:0.453552:0.660628:0.437191:0.651359:0.437191:0.000000
x:@0.764099:0.453552:0.771562:0.453552:0.771562:0.437191:0.764099:0.437191:0.000000
la palabra ‘exponente’ por la palabra ‘logaritmo’ se obtiene::@0.287490:0.470149:0.711450:0.470149:0.711450:0.453760:0.287490:0.453760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.491014:0.496735:0.498474:0.496735:0.498474:0.480420:0.491014:0.480420:0.000000
x:@0.556740:0.496735:0.564182:0.496735:0.564182:0.480420:0.556740:0.480420:0.000000
a:@0.539143:0.498743:0.544500:0.498743:0.544500:0.489288:0.539143:0.489288:0.000000
=:@0.503164:0.496321:0.513252:0.496321:0.513252:0.479427:0.503164:0.479427:0.000000
():@0.548278:0.498076:0.572717:0.498076:0.572717:0.476486:0.548278:0.476486:0.000000:0.000000
log:@0.515601:0.496735:0.539378:0.496735:0.539378:0.480393:0.515601:0.480393:0.000000:0.000000:0.000000
y:@0.693982:0.489794:0.698306:0.489794:0.698306:0.480340:0.693982:0.480340:0.000000
   = :@0.652853:0.497424:0.683245:0.497424:0.683245:0.481082:0.652853:0.481082:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.656859:0.497424:0.664301:0.497424:0.664301:0.481109:0.656859:0.481109:0.000000
a:@0.683429:0.497424:0.692671:0.497424:0.692671:0.481109:0.683429:0.481109:0.000000
si y solo sí:@0.578050:0.497217:0.649895:0.497217:0.649895:0.480875:0.578050:0.480875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función logarítmica con base   es la función inversa de la función exponencial :@0.287495:0.524080:0.907604:0.524080:0.907604:0.507691:0.287495:0.507691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.534555:0.524080:0.543824:0.524080:0.543824:0.507718:0.534555:0.507718:0.000000
con base  .:@0.287495:0.540676:0.370291:0.540676:0.370291:0.524287:0.287495:0.524287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.357815:0.540676:0.367084:0.540676:0.367084:0.524315:0.357815:0.524315:0.000000
Gráficas de la función logarítmica y exponencial:@0.287495:0.580561:0.770276:0.580561:0.770276:0.559051:0.287495:0.559051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.287495:0.610471:0.293263:0.610471:0.293263:0.593571:0.287495:0.593571:0.000000
 :@0.293263:0.610471:0.297299:0.610471:0.297299:0.594082:0.293263:0.594082:0.000000
El dominio de la función logaritmo son los reales positivos, es decir, no existen :@0.315988:0.610471:0.907644:0.610471:0.907644:0.594082:0.315988:0.594082:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmos de números negativos.:@0.315985:0.627068:0.566265:0.627068:0.566265:0.610679:0.315985:0.610679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.287495:0.650787:0.293263:0.650787:0.293263:0.633886:0.287495:0.633886:0.000000
 :@0.293263:0.650787:0.297299:0.650787:0.297299:0.634398:0.293263:0.634398:0.000000
El rango o recorrido es el conjunto de los números reales.:@0.315988:0.650787:0.735044:0.650787:0.735044:0.634398:0.315988:0.634398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.287495:0.675294:0.293263:0.675294:0.293263:0.658393:0.287495:0.658393:0.000000
 :@0.293263:0.675294:0.297299:0.675294:0.297299:0.658905:0.293263:0.658905:0.000000
La función :@0.315988:0.675294:0.396922:0.675294:0.396922:0.658905:0.315988:0.658905:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.401109:0.675773:0.408590:0.675773:0.408590:0.659412:0.401109:0.659412:0.000000
x:@0.467024:0.675773:0.474487:0.675773:0.474487:0.659412:0.467024:0.659412:0.000000
a:@0.449377:0.677777:0.454749:0.677777:0.454749:0.668295:0.449377:0.668295:0.000000
=:@0.413306:0.675358:0.423423:0.675358:0.423423:0.658416:0.413306:0.658416:0.000000
():@0.458537:0.677108:0.483046:0.677108:0.483046:0.655456:0.458537:0.655456:0.000000:0.000000
log:@0.425766:0.675773:0.449612:0.675773:0.449612:0.659384:0.425766:0.659384:0.000000:0.000000:0.000000
 corta al eje   en el punto (0, 1); no corta al eje  . :@0.485711:0.675303:0.839299:0.675303:0.839299:0.658914:0.485711:0.658914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.573943:0.675303:0.581406:0.675303:0.581406:0.658941:0.573943:0.658941:0.000000
y:@0.824575:0.675303:0.832057:0.675303:0.832057:0.658941:0.824575:0.658941:0.000000
•:@0.287504:0.699022:0.293272:0.699022:0.293272:0.682121:0.287504:0.682121:0.000000
 :@0.293272:0.699022:0.297307:0.699022:0.297307:0.682633:0.293272:0.682633:0.000000
La asíntota vertical es   = 0, es decir, el eje   es asíntota vertical.:@0.315997:0.699022:0.774194:0.699022:0.774194:0.682633:0.315997:0.682633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.476076:0.699022:0.483539:0.699022:0.483539:0.682660:0.476076:0.682660:0.000000
y:@0.624287:0.699022:0.631769:0.699022:0.631769:0.682660:0.624287:0.682660:0.000000
•:@0.287504:0.724414:0.293272:0.724414:0.293272:0.707513:0.287504:0.707513:0.000000
 :@0.293272:0.724414:0.297307:0.724414:0.297307:0.708025:0.293272:0.708025:0.000000
La función  :@0.315997:0.724414:0.399824:0.724414:0.399824:0.708025:0.315997:0.708025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.403434:0.724896:0.410915:0.724896:0.410915:0.708534:0.403434:0.708534:0.000000
x:@0.469349:0.724896:0.476813:0.724896:0.476813:0.708534:0.469349:0.708534:0.000000
a:@0.451701:0.726900:0.457073:0.726900:0.457073:0.717417:0.451701:0.717417:0.000000
=:@0.415631:0.724481:0.425748:0.724481:0.425748:0.707539:0.415631:0.707539:0.000000
():@0.460863:0.726231:0.485371:0.726231:0.485371:0.704579:0.460863:0.704579:0.000000:0.000000
log:@0.428090:0.724896:0.451935:0.724896:0.451935:0.708507:0.428090:0.708507:0.000000:0.000000:0.000000
  es creciente en el intervalo de  0,:@0.488035:0.724425:0.735426:0.724010:0.735426:0.707622:0.488035:0.708036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+∞:@0.737656:0.723596:0.760838:0.723596:0.760838:0.706653:0.737656:0.706653:0.000000:0.000000
]:@0.717397:0.725603:0.723534:0.725603:0.723534:0.703138:0.717397:0.703138:0.000000
[:@0.760794:0.725603:0.766931:0.725603:0.766931:0.703138:0.760794:0.703138:0.000000
 con a >1:@0.769433:0.724004:0.837689:0.724004:0.837689:0.707615:0.769433:0.707615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.805106:0.724420:0.814375:0.724420:0.814375:0.708059:0.805106:0.708059:0.000000
 > 1 y decre-:@0.814375:0.724420:0.903639:0.724420:0.903639:0.708031:0.814375:0.708031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciente en el intervalo de  0,:@0.315981:0.742441:0.517616:0.742275:0.517616:0.725886:0.315981:0.726052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+∞:@0.519846:0.741860:0.543028:0.741860:0.543028:0.724918:0.519846:0.724918:0.000000:0.000000
]:@0.499608:0.743872:0.505744:0.743872:0.505744:0.721407:0.499608:0.721407:0.000000
[:@0.543005:0.743872:0.549141:0.743872:0.549141:0.721407:0.543005:0.721407:0.000000
 si 0 < a >1:@0.551644:0.742274:0.630256:0.742274:0.630256:0.725885:0.551644:0.725885:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.598534:0.742440:0.607803:0.742440:0.607803:0.726079:0.598534:0.726079:0.000000
 < 1.:@0.607803:0.742440:0.639056:0.742440:0.639056:0.726051:0.607803:0.726051:0.000000:0.000000:0.000000:0.000000:0.000000
Propiedades:@0.287495:0.775198:0.414566:0.775198:0.414566:0.753688:0.287495:0.753688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para cualquier par de números reales positivos  ,:@0.287495:0.799455:0.658757:0.799234:0.658757:0.782845:0.287495:0.783066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mn:@0.641159:0.799234:0.670201:0.799234:0.670201:0.782872:0.641159:0.782872:0.000000:0.000000
∈:@0.671104:0.798819:0.684242:0.798819:0.684242:0.781877:0.671104:0.781877:0.000000
+:@0.700099:0.791335:0.705962:0.791335:0.705962:0.781516:0.700099:0.781516:0.000000
:@0.685859:0.800107:0.699164:0.800107:0.699164:0.783359:0.685859:0.783359:0.000000
 se cumplen las siguientes :@0.706774:0.799457:0.907654:0.799457:0.907654:0.783068:0.706774:0.783068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades::@0.287490:0.816054:0.383093:0.816054:0.383093:0.799665:0.287490:0.799665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.287490:0.840741:0.301717:0.840741:0.301717:0.823840:0.287490:0.823840:0.000000:0.000000
1)log:@0.299237:0.841033:0.340406:0.841033:0.340406:0.824644:0.299237:0.824644:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.355257:0.841033:0.364250:0.841033:0.364250:0.824644:0.355257:0.824644:0.000000
0:@0.384622:0.841033:0.393615:0.841033:0.393615:0.824644:0.384622:0.824644:0.000000
 :@0.310806:0.841033:0.314842:0.841033:0.314842:0.824644:0.310806:0.824644:0.000000
a:@0.340175:0.843036:0.345547:0.843036:0.345547:0.833554:0.340175:0.833554:0.000000
():@0.349337:0.842368:0.368410:0.842368:0.368410:0.820715:0.349337:0.820715:0.000000:0.000000
=:@0.371586:0.840618:0.381703:0.840618:0.381703:0.823675:0.371586:0.823675:0.000000
4.:@0.572410:0.840742:0.586636:0.840742:0.586636:0.823841:0.572410:0.823841:0.000000:0.000000
4) log:@0.581441:0.841033:0.625756:0.841033:0.625756:0.824644:0.581441:0.824644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.688613:0.841033:0.712440:0.841033:0.712440:0.824644:0.688613:0.824644:0.000000:0.000000:0.000000
log:@0.764867:0.841033:0.788712:0.841033:0.788712:0.824644:0.764867:0.824644:0.000000:0.000000:0.000000
 :@0.596153:0.841033:0.600189:0.841033:0.600189:0.824644:0.596153:0.824644:0.000000
a:@0.625522:0.843036:0.630894:0.843036:0.630894:0.833554:0.625522:0.833554:0.000000
a:@0.712219:0.843036:0.717591:0.843036:0.717591:0.833554:0.712219:0.833554:0.000000
a:@0.788493:0.843036:0.793865:0.843036:0.793865:0.833554:0.788493:0.833554:0.000000
mn:@0.642013:0.841033:0.666190:0.841033:0.666190:0.824671:0.642013:0.824671:0.000000:0.000000
m:@0.728707:0.841033:0.743338:0.841033:0.743338:0.824671:0.728707:0.824671:0.000000
n:@0.804979:0.841033:0.814487:0.841033:0.814487:0.824671:0.804979:0.824671:0.000000
(:@0.634684:0.842368:0.640820:0.842368:0.640820:0.820715:0.634684:0.820715:0.000000
):@0.666822:0.842368:0.672958:0.842368:0.672958:0.820715:0.666822:0.820715:0.000000
=:@0.676146:0.840618:0.686263:0.840618:0.686263:0.823675:0.676146:0.823675:0.000000
():@0.721377:0.842368:0.750180:0.842368:0.750180:0.820715:0.721377:0.820715:0.000000:0.000000
+:@0.752735:0.840618:0.762851:0.840618:0.762851:0.823675:0.752735:0.823675:0.000000
():@0.797653:0.842368:0.821277:0.842368:0.821277:0.820715:0.797653:0.820715:0.000000:0.000000
2.:@0.287495:0.878211:0.301722:0.878211:0.301722:0.861310:0.287495:0.861310:0.000000:0.000000
2)log:@0.297435:0.878508:0.341168:0.878508:0.341168:0.862119:0.297435:0.862119:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.389094:0.878508:0.398086:0.878508:0.398086:0.862119:0.389094:0.862119:0.000000
 :@0.311569:0.878508:0.315604:0.878508:0.315604:0.862119:0.311569:0.862119:0.000000
a:@0.340937:0.880512:0.346309:0.880512:0.346309:0.871029:0.340937:0.871029:0.000000
a:@0.357428:0.878508:0.366697:0.878508:0.366697:0.862146:0.357428:0.862146:0.000000
():@0.350099:0.879843:0.374037:0.879843:0.374037:0.858191:0.350099:0.858191:0.000000:0.000000
=:@0.377218:0.878093:0.387335:0.878093:0.387335:0.861151:0.377218:0.861151:0.000000
5.:@0.572422:0.878217:0.586648:0.878217:0.586648:0.861317:0.572422:0.861317:0.000000:0.000000
5) log:@0.583241:0.878083:0.626718:0.878083:0.626718:0.861694:0.583241:0.861694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.686995:0.878083:0.710840:0.878083:0.710840:0.861694:0.686995:0.861694:0.000000:0.000000:0.000000
log:@0.762954:0.878083:0.786799:0.878083:0.786799:0.861694:0.762954:0.861694:0.000000:0.000000:0.000000
 :@0.597113:0.878083:0.601149:0.878083:0.601149:0.861694:0.597113:0.861694:0.000000
a:@0.626484:0.880087:0.631855:0.880087:0.631855:0.870604:0.626484:0.870604:0.000000
a:@0.710618:0.880087:0.715990:0.880087:0.715990:0.870604:0.710618:0.870604:0.000000
a:@0.786572:0.880087:0.791943:0.880087:0.791943:0.870604:0.786572:0.870604:0.000000
m:@0.646429:0.869321:0.661060:0.869321:0.661060:0.852959:0.646429:0.852959:0.000000
n:@0.648990:0.888932:0.658499:0.888932:0.658499:0.872571:0.648990:0.872571:0.000000
m:@0.727102:0.878083:0.741733:0.878083:0.741733:0.861721:0.727102:0.861721:0.000000
n:@0.803060:0.878083:0.812569:0.878083:0.812569:0.861721:0.803060:0.861721:0.000000
:@0.635644:0.870163:0.642720:0.870163:0.642720:0.853221:0.635644:0.853221:0.000000
:@0.635644:0.889926:0.642720:0.889926:0.642720:0.872984:0.635644:0.872984:0.000000
:@0.635644:0.881242:0.642720:0.881242:0.642720:0.864300:0.635644:0.864300:0.000000
:@0.664078:0.870164:0.671154:0.870164:0.671154:0.853222:0.664078:0.853222:0.000000
:@0.664071:0.889926:0.671147:0.889926:0.671147:0.872984:0.664071:0.872984:0.000000
:@0.664071:0.881242:0.671147:0.881242:0.671147:0.864300:0.664071:0.864300:0.000000
=:@0.674538:0.877660:0.684655:0.877660:0.684655:0.860718:0.674538:0.860718:0.000000
():@0.719773:0.879416:0.748575:0.879416:0.748575:0.857764:0.719773:0.857764:0.000000:0.000000
−:@0.751131:0.877668:0.761248:0.877668:0.761248:0.860726:0.751131:0.860726:0.000000
():@0.795735:0.879416:0.819359:0.879416:0.819359:0.857764:0.795735:0.857764:0.000000:0.000000
3.:@0.287495:0.917181:0.301722:0.917181:0.301722:0.900281:0.287495:0.900281:0.000000:0.000000
3) log:@0.296669:0.917741:0.340408:0.917741:0.340408:0.901352:0.296669:0.901352:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.310805:0.917741:0.314840:0.917741:0.314840:0.901352:0.310805:0.901352:0.000000
a:@0.340173:0.919745:0.345545:0.919745:0.345545:0.910262:0.340173:0.910262:0.000000
x:@0.367033:0.910078:0.371358:0.910078:0.371358:0.900596:0.367033:0.900596:0.000000
a:@0.356611:0.917741:0.365880:0.917741:0.365880:0.901379:0.356611:0.901379:0.000000
x:@0.399179:0.917741:0.406642:0.917741:0.406642:0.901379:0.399179:0.901379:0.000000
( ):@0.349335:0.920713:0.381547:0.920713:0.381547:0.894097:0.349335:0.894097:0.000000:0.000000:0.000000
=:@0.384725:0.917326:0.394841:0.917326:0.394841:0.900384:0.384725:0.900384:0.000000
6.:@0.572410:0.917187:0.586636:0.917187:0.586636:0.900287:0.572410:0.900287:0.000000:0.000000
5) log:@0.582766:0.916924:0.626237:0.916924:0.626237:0.900535:0.582766:0.900535:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
log:@0.697460:0.916924:0.721309:0.916924:0.721309:0.900535:0.697460:0.900535:0.000000:0.000000:0.000000
 :@0.596639:0.916924:0.600675:0.916924:0.600675:0.900535:0.596639:0.900535:0.000000
a:@0.626008:0.918928:0.631380:0.918928:0.631380:0.909446:0.626008:0.909446:0.000000
k:@0.656947:0.909261:0.661336:0.909261:0.661336:0.899779:0.656947:0.899779:0.000000
a:@0.721078:0.918928:0.726450:0.918928:0.726450:0.909446:0.721078:0.909446:0.000000
m:@0.642447:0.916924:0.657078:0.916924:0.657078:0.900563:0.642447:0.900563:0.000000
k:@0.687687:0.916924:0.695260:0.916924:0.695260:0.900563:0.687687:0.900563:0.000000
m:@0.737570:0.916924:0.752202:0.916924:0.752202:0.900563:0.737570:0.900563:0.000000
( ):@0.635170:0.919896:0.671454:0.919896:0.671454:0.893280:0.635170:0.893280:0.000000:0.000000:0.000000
=:@0.674642:0.916509:0.684758:0.916509:0.684758:0.899567:0.674642:0.899567:0.000000
():@0.730240:0.918259:0.759042:0.918259:0.759042:0.896606:0.730240:0.896606:0.000000:0.000000
Pienso y progreso:@0.294883:0.334661:0.417347:0.334661:0.417347:0.319297:0.294883:0.319297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Por qué es importante conocer el pH de una solución?:@0.294883:0.352056:0.664171:0.352056:0.664171:0.337157:0.294883:0.337157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un equipo de científicos ambientales está estudiando el pH del agua en un lago. :@0.287495:0.168345:0.907696:0.168345:0.907696:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.443373:0.168345:0.447409:0.168345:0.447409:0.151956:0.443373:0.151956:0.000000
El pH se mide utilizando una escala logarítmica, donde un pH de 7 es neutro; valores :@0.287495:0.184941:0.907713:0.184941:0.907713:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inferiores a 7 son ácidos; y superiores a 7 son alcalinos. Si el pH del lago es de 6,5, ¿cuál :@0.287495:0.201538:0.907584:0.201538:0.907584:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es la concentración de iones del hidrógeno en el agua?:@0.287495:0.218134:0.691905:0.218134:0.691905:0.201745:0.287495:0.201745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ecuación que relaciona el pH con la concentración de iones de hidrógeno (H ) :@0.287495:0.241853:0.886394:0.241858:0.886394:0.225469:0.287495:0.225464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.871072:0.235811:0.877475:0.235811:0.877475:0.226256:0.871072:0.226256:0.000000
es::@0.287495:0.258455:0.306513:0.258455:0.306513:0.242066:0.287495:0.242066:0.000000:0.000000:0.000000
pH:@0.532251:0.277568:0.552577:0.277568:0.552577:0.261207:0.532251:0.261207:0.000000:0.000000
H:@0.626693:0.277568:0.637805:0.277568:0.637805:0.261207:0.626693:0.261207:0.000000
=−:@0.556797:0.277153:0.580532:0.277153:0.580532:0.260211:0.556797:0.260211:0.000000:0.000000
:@0.619359:0.276558:0.626435:0.276558:0.626435:0.259616:0.619359:0.259616:0.000000
:@0.619359:0.282492:0.626435:0.282492:0.626435:0.265550:0.619359:0.265550:0.000000
:@0.648309:0.276558:0.655385:0.276558:0.655385:0.259616:0.648309:0.259616:0.000000
:@0.648309:0.282492:0.655385:0.282492:0.655385:0.265550:0.648309:0.265550:0.000000
+:@0.639195:0.269663:0.645058:0.269663:0.645058:0.259844:0.639195:0.259844:0.000000
log:@0.581609:0.277566:0.605454:0.277566:0.605454:0.261177:0.581609:0.261177:0.000000:0.000000:0.000000
10:@0.604382:0.279569:0.614720:0.279569:0.614720:0.270071:0.604382:0.270071:0.000000:0.000000
.:@0.659298:0.277823:0.662505:0.277823:0.662505:0.261434:0.659298:0.261434:0.000000
Donde [H ] es la concentración de iones del hidrógeno en moles por litro (mol/L).:@0.287502:0.301542:0.885107:0.301547:0.885107:0.285158:0.287502:0.285153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.358698:0.295500:0.365101:0.295500:0.365101:0.285945:0.358698:0.285945:0.000000
nidad de conocimientos:@0.306727:0.388722:0.480398:0.388722:0.480398:0.373358:0.306727:0.373358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.389508:0.297460:0.389508:0.297460:0.372372:0.284892:0.372372:0.000000
Funciones logarítmicas:@0.286308:0.075160:0.626961:0.075160:0.626961:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108603:0.183816:0.108603:0.183816:0.011514:0.094760:0.011514:0.000000:0.000000
–2:@0.074577:0.722074:0.088153:0.722074:0.088153:0.708746:0.074577:0.708746:0.000000:0.000000
2:@0.080367:0.683465:0.087242:0.683465:0.087242:0.670137:0.080367:0.670137:0.000000
4:@0.080367:0.663473:0.087242:0.663473:0.087242:0.650145:0.080367:0.650145:0.000000
6:@0.080367:0.643936:0.087242:0.643936:0.087242:0.630608:0.080367:0.630608:0.000000
–2 0:@0.060251:0.710842:0.087497:0.710842:0.087497:0.697514:0.060251:0.697514:0.000000:0.000000:0.000000:0.000000
2:@0.112800:0.710842:0.119675:0.710842:0.119675:0.697514:0.112800:0.697514:0.000000
4:@0.137687:0.710842:0.144562:0.710842:0.144562:0.697514:0.137687:0.697514:0.000000
6:@0.161301:0.710842:0.168176:0.710842:0.168176:0.697514:0.161301:0.697514:0.000000
8 10 12:@0.184594:0.710842:0.242155:0.710842:0.242155:0.697514:0.184594:0.697514:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.080070:0.627827:0.085242:0.627827:0.085242:0.616155:0.080070:0.616155:0.000000
x:@0.252288:0.709083:0.257460:0.709083:0.257460:0.697411:0.252288:0.697411:0.000000
(0, 1):@0.059396:0.691425:0.083002:0.691425:0.083002:0.679763:0.059396:0.679763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y a:@0.103817:0.628865:0.127071:0.628865:0.127071:0.617194:0.103817:0.617194:0.000000:0.000000:0.000000
 = :@0.108988:0.628865:0.120949:0.628865:0.120949:0.617203:0.108988:0.617203:0.000000:0.000000:0.000000
x:@0.127064:0.624620:0.130230:0.624620:0.130230:0.617821:0.127064:0.617821:0.000000
y y y x:@0.179819:0.637648:0.202124:0.637648:0.202124:0.625976:0.179819:0.625976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =   = :@0.184991:0.637648:0.196952:0.637648:0.196952:0.625986:0.184991:0.625986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 =   = :@0.184991:0.637648:0.196952:0.637648:0.196952:0.625986:0.184991:0.625986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.046926:0.727300:0.053188:0.727300:0.053188:0.715628:0.046926:0.715628:0.000000
(1, 0):@0.119178:0.696705:0.142784:0.696705:0.142784:0.685043:0.119178:0.685043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.193197:0.681249:0.198368:0.681249:0.198368:0.669577:0.193197:0.669577:0.000000
 = log ( ):@0.198368:0.681249:0.241492:0.681249:0.241492:0.669587:0.198368:0.669587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.226091:0.683467:0.229660:0.683467:0.229660:0.676663:0.226091:0.676663:0.000000
x:@0.232990:0.681249:0.238161:0.681249:0.238161:0.669577:0.232990:0.669577:0.000000
0:@0.080622:0.710841:0.087497:0.710841:0.087497:0.697513:0.080622:0.697513:0.000000
–2:@0.098324:0.870316:0.111900:0.870316:0.111900:0.858226:0.098324:0.858226:0.000000:0.000000
2:@0.104113:0.835293:0.110988:0.835293:0.110988:0.823203:0.104113:0.823203:0.000000
4:@0.104113:0.817158:0.110988:0.817158:0.110988:0.805067:0.104113:0.805067:0.000000
6:@0.104113:0.799435:0.110988:0.799435:0.110988:0.787345:0.104113:0.787345:0.000000
–4 –2 0:@0.060530:0.860127:0.111243:0.860127:0.111243:0.848037:0.060530:0.848037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.136546:0.860127:0.143421:0.860127:0.143421:0.848037:0.136546:0.848037:0.000000
4:@0.161433:0.860127:0.168308:0.860127:0.168308:0.848037:0.161433:0.848037:0.000000
6:@0.185047:0.860127:0.191923:0.860127:0.191923:0.848037:0.185047:0.848037:0.000000
8 10:@0.208340:0.860127:0.242086:0.860127:0.242086:0.848037:0.208340:0.848037:0.000000:0.000000:0.000000:0.000000
y:@0.103817:0.784822:0.108988:0.784822:0.108988:0.774235:0.103817:0.774235:0.000000
x:@0.252288:0.858532:0.257460:0.858532:0.257460:0.847944:0.252288:0.847944:0.000000
(0, 1):@0.086918:0.844978:0.110524:0.844978:0.110524:0.834399:0.086918:0.834399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.055878:0.808735:0.061049:0.808735:0.061049:0.798147:0.055878:0.798147:0.000000
 = :@0.061049:0.808735:0.073011:0.808735:0.073011:0.798156:0.061049:0.798156:0.000000:0.000000:0.000000
a:@0.073011:0.808735:0.079132:0.808735:0.079132:0.798147:0.073011:0.798147:0.000000
x:@0.079130:0.804883:0.082295:0.804883:0.082295:0.798715:0.079130:0.798715:0.000000
y y y:@0.172148:0.787416:0.177320:0.787416:0.177320:0.776828:0.172148:0.776828:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.177320:0.787416:0.189281:0.787416:0.189281:0.776837:0.177320:0.776837:0.000000:0.000000:0.000000
 = :@0.177320:0.787416:0.189281:0.787416:0.189281:0.776837:0.177320:0.776837:0.000000:0.000000:0.000000
x:@0.189281:0.787416:0.194453:0.787416:0.194453:0.776828:0.189281:0.776828:0.000000
h:@0.070672:0.874975:0.076935:0.874975:0.076935:0.864387:0.070672:0.864387:0.000000
(1, 0):@0.134759:0.844520:0.158365:0.844520:0.158365:0.833941:0.134759:0.833941:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.197801:0.870607:0.202973:0.870607:0.202973:0.860019:0.197801:0.860019:0.000000
 = log ( ):@0.202973:0.870607:0.246099:0.870604:0.246099:0.860025:0.202973:0.860028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.230698:0.872619:0.234267:0.872619:0.234267:0.866446:0.230698:0.866446:0.000000
x:@0.237597:0.870604:0.242768:0.870604:0.242768:0.860017:0.237597:0.860017:0.000000
2 2 2:@0.104113:0.835293:0.110988:0.835293:0.110988:0.823203:0.104113:0.823203:0.000000:0.000000:0.000000:0.000000:0.000000
2 2 2:@0.136546:0.860127:0.143421:0.860127:0.143421:0.848037:0.136546:0.848037:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.104368:0.860127:0.111243:0.860127:0.111243:0.848037:0.104368:0.848037:0.000000
El pH permite analizar:@0.073803:0.352707:0.204793:0.352707:0.204793:0.339298:0.073803:0.339298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el agua del lago.:@0.073803:0.366286:0.171714:0.366286:0.171714:0.352877:0.073803:0.352877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.134435:0.756121:0.142862:0.756121:0.142862:0.741247:0.134435:0.741247:0.000000
 > 1:@0.142862:0.756121:0.168359:0.756121:0.168359:0.741222:0.142862:0.741222:0.000000:0.000000:0.000000:0.000000
0 <   < 1:@0.121687:0.903187:0.181108:0.903187:0.181108:0.888288:0.121687:0.888288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.147184:0.903187:0.155611:0.903187:0.155611:0.888313:0.147184:0.888313:0.000000
M.5.1.75.:@0.298180:0.954519:0.353208:0.954519:0.353208:0.942057:0.298180:0.942057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.353207:0.954519:0.359680:0.954519:0.359680:0.942228:0.353207:0.942228:0.000000:0.000000
Reconocer la función logarítmica como la función inversa de la función exponencial para calcular el :@0.360601:0.954519:0.906607:0.954519:0.906607:0.942600:0.360601:0.942600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
logaritmo de un número y graficarla analizando esta relación para determinar sus características.:@0.298180:0.965835:0.810273:0.965835:0.810273:0.953916:0.298180:0.953916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.462458:0.965835:0.465393:0.965835:0.465393:0.953916:0.462458:0.953916:0.000000