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Jan 3, 2026

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Propiedades de los Logaritmos: Explicación Fácil

Damba Kangama Dembele

@damba

Los logaritmos son herramientas matemáticas fundamentales que permiten expresar potencias... Show more

TEORIA
Y
EJERCICIOS

•log N=x b =N
• base 10 = log N → no se indica la base
- base n° irracional e = In N

LOGARITMOS
Ejemplo: $log_2 8 = 3

Logaritmos y sus propiedades

Un logaritmo es simplemente otra forma de expresar una potencia. Por ejemplo, log₂ 8 = 3 significa que 2³ = 8. Cuando no se indica la base, se asume que es 10, y cuando usamos la base e (número irracional), se escribe como ln N.

Las propiedades de los logaritmos son claves para resolver problemas:

El logaritmo de un número en su misma base es 1 $log_a a = 1$
El logaritmo de 1 en cualquier base es 0 $log_a 1 = 0$
El logaritmo de una potencia es el exponente multiplicado por el logaritmo de la base $log_a m^n = n·log_a m$
El logaritmo de un producto es la suma de logaritmos $log_a (m·n) = log_a m + log_a n$
El logaritmo de una división es la resta de logaritmos $log_a (m/n) = log_a m - log_a n$

💡 Truco práctico: Cuando veas un logaritmo, piensa siempre: "¿A qué exponente debo elevar la base para obtener ese número?" Así conectarás inmediatamente con la potencia correspondiente.

Para resolver ejercicios de logaritmos, normalmente convertirás la expresión logarítmica a una expresión exponencial. Por ejemplo, para calcular log₃ 9, piensas: "¿A qué exponente debo elevar 3 para obtener 9?". Como 3² = 9, entonces log₃ 9 = 2.

Recuerda que los logaritmos de números negativos no existen en los números reales, y que puedes aplicar las propiedades de potencias dentro de los logaritmos, como cuando trabajas con raíces (que son potencias fraccionarias).

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Matemáticas

•

Jan 3, 2026

•

1 page

Propiedades de los Logaritmos: Explicación Fácil

Damba Kangama Dembele

@damba

Los logaritmos son herramientas matemáticas fundamentales que permiten expresar potencias de forma diferente. Con la fórmula log_b N = x, estamos diciendo que b^x = N. Dominar los logaritmos y sus propiedades te permitirá resolver muchos problemas matemáticos con facilidad.

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Logaritmos y sus propiedades

Las propiedades de los logaritmos son claves para resolver problemas:

El logaritmo de un número en su misma base es 1 $log_a a = 1$
El logaritmo de 1 en cualquier base es 0 $log_a 1 = 0$
El logaritmo de una potencia es el exponente multiplicado por el logaritmo de la base $log_a m^n = n·log_a m$
El logaritmo de un producto es la suma de logaritmos $log_a (m·n) = log_a m + log_a n$
El logaritmo de una división es la resta de logaritmos $log_a (m/n) = log_a m - log_a n$

💡 Truco práctico: Cuando veas un logaritmo, piensa siempre: "¿A qué exponente debo elevar la base para obtener ese número?" Así conectarás inmediatamente con la potencia correspondiente.