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Ludo: Logaritmos en juego

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Ludo: Logaritmos en juego

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Trivia matemática de logaritmos

Created by

Eduardo Daniel Cortez
Eduardo Daniel Cortez
El Salvador

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Ludo: Logaritmos en juego
 

Ludo: Logaritmos en juegoOnline version

Trivia matemática de logaritmos

by Eduardo Daniel Cortez
1

1) Si f(x)=x^3, ¿cuál es dominio y rango de f^{-1}?

2

2) ¿Qué significa log_b(a)?

3

3) Propiedad: log_b(xy)=

4

4) Cambio de base: log_b(a)=?

5

5) Definición de logaritmo y su gráfica: dominio de log_b(x) es?

6

6) Relación exponencial y logarítmica: si y=log_b(x), ¿quién es x?

7

7) Evaluación: log_2(8)=

8

8) Propiedad: log_b(1)=

9

9) Cambio de base: log_3(12)≈

10

10) Si f(x)=sqrt(x), ¿dominio y rango de f^{-1}?

Explicación

La inversa de una función creciente y biyectiva como x^3 tiene dominio y rango reales.

Por definición, b^log_b(a)=a.

Una de las propiedades básicas de logaritmos es la suma para productos.

Usa cualquier base k para convertir logs.

El logaritmo solo está definido para x>0.

La definición dice que b elevado al logaritmo da la x original.

2^3=8, por tanto log_2(8)=3.

Cualquier base log de 1 es 0.

Usa fórmula ln(12)/ln(3) ≈ 2.262.

La inversa es f^{-1}(x)=x^2 con x≥0, así que dominio y rango son [0,∞).

 
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