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Desafío de Ecuaciones Exponenciales y Logaritmos

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Desafío de Ecuaciones Exponenciales y Logaritmos

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Quiz de logaritmos y exponenciales

Created by

adrian
adrian
Bolivia

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Desafío de Ecuaciones Exponenciales y Logaritmos
 

Desafío de Ecuaciones Exponenciales y LogaritmosOnline version

Quiz de logaritmos y exponenciales

by adrian
1

La ecuación 2^(3x)=8 tiene solución x=1.

2

log base 10 de 1000 es igual a 2.

3

ln(e^2)=2.

4

log_b(b)=1 para cualquier base b>0, b≠1.

5

log_2(8)=2.

6

La ecuación e^(x)=0 no tiene solución real.

7

log_5(25)=2.

8

Si log_a(x)=0 entonces x=1, para cualquier base a>0, a≠1.

9

La propiedad log_b(xy)=log_b x + log_b y es válida para todas las bases y positivos x,y.

10

Si 2^{y+1} = 8, ¿cuál es y?

11

Resuelve 3^{2z} = 9^{z}

12

Encuentra el valor de t si 5^{t-1} = 125

13

Si a^{m} = a^{n} con a>0 y a≠1, ¿qué se deduce de m y n?

14

¿Qué valor tiene x si (2^{x})^{3} = 2^{9}?

15

Resuelve (1/2)^{p} = 4^{-1}

16

Si log_{2}(x) = 4, ¿cuál es x?

17

¿Qué expresa 7^{q} = 7^{q+2}?

18

Encuentra k si 10^{2k} = 100

19

Si (3^{r})^{2} = 3^{6}, ¿cuál es r?

20

Qué implica 6^{x} = 6^{y} con base positiva y diferente de 1?

21

Resuelve (2^{x})^{0} = 1. ¿Cuál es x?

22

Si log_{3}(9) = s, ¿cuál es s?

Explicación

2^(3x)=8 => 3x=log2(8)=3 => x=1. Es verdadera.

log10(1000)=3, no 2. Es falsa.

Por propiedades del logaritmo: ln(e^a)=a, aquí a=2.

Propiedad de logaritmos: log_b(b)=1 para cualquier base válida.

2^3=8, por lo que log_2(8)=3, no 2.

La exponencial nunca es 0, por eso no tiene solución real.

5^2=25, por lo tanto el logaritmo es 2.

Cualquier base logarítmica: log_a(1)=0.

Propiedad fundamental de logaritmos válida para x,y>0.

 
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