Question

O logaritmo de 7 na base raiz quíntupla de 7 ??
( como a imagem )

Answer 1

Pode ser assim:

$log_{\sqrt[5]{7}}7=\frac{log_77}{log_7 \sqrt[5]{7}}=\frac{log_77}{log_7 7^{\frac{1}{5}}}=\frac{log_77}{{\frac{1}{5}}.log_7 7}=\frac{1}{\frac{1}{5}.1}=\\\\ =\frac{1}{\frac{1}{5}}=1.\frac{5}{1}=5$

Ou

$log_{\sqrt[5]{7}}7=?\\\\ log_{\sqrt[5]{7}}7=x\\\\ (\sqrt[5]{7})^x=7\\\\ (7)^{\frac{x}{5}}=7^1\\\\ \frac{x}{5}=1\\ x=5$

Answer 2

$log_{ \sqrt[5]{7} }\ 7= \frac{log_7 \ 7}{log_{7} \ \sqrt[5]{7}} } =\frac{log_7 \ 7}{log_{7} \ 7^{ \frac{1}{5} }} } =\frac{log_7 \ 7}{ \frac{1}{5} \cdot \ log_{7} \ 7}} } =\frac{1}{ \frac{1}{5} \cdot \ 1 } =1\cdot \frac{5}{1} =5$