Question

1) Obtenha o logaritmo em cada item a seguir:
a) log381 = x

b) log832 = x

c) log 1000 = x

d) log 0,000000001 = x

e) log125625 = x

f) log7343 = x

g) log11121 = x

h) log1281024 = x

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:log_3\:81 = x \iff 3^x = 81 \iff \not3^x = \not3^4 \iff x = 4}$

$\mathsf{b)\:log_8\:32 = x \iff log_{2^3}\:2^5 = x \iff x = \dfrac{5}{3}\:log_2\:2 \iff x = \dfrac{5}{3}}$

$\mathsf{c)\:log\:1000 = x \iff 10^x = 1000 \iff \not10^x = \not10^3 \iff x = 3}$

$\mathsf{d)\:log\:0,000000001 = x \iff 10^x = 10^{-9} \iff x = -9}$

$\mathsf{e)\:log_{125}\:625 = x \iff log_{5^3}\:5^4 = x \iff x = \dfrac{4}{3}\:log_5\:5 \iff x = \dfrac{4}{3}}$

$\mathsf{f)\:log_7\:343 = x \iff 7^x = 343 \iff \not7^x = \not7^3 \iff x = 3}$

$\mathsf{g)\:log_{11}\:121 = x \iff 11^x = 121 \iff \not11^x = \not11^2 \iff x = 2}$

$\mathsf{h)\:log_{128}\:1024 = x \iff log_{2^7}\:2^{10} = x \iff x = \dfrac{10}{7}\:log_2\:2 \iff x = \dfrac{10}{7}}$