Question

Se log de x na base 2 é igual à a. Determine log de x na base 8:

Answer 1

$log_{2}(x)=a$

Mudando a base do logaritmo para 8:

$\dfrac{log_{8}(x)}{log_{8}(2)}=a~~~~\therefore~~~~log_{8}(x)=a\cdot log_{8}(2)$

Utilizando a propriedade $log_{b}(a)=\dfrac{1}{log_{a}(b)}$:

$log_{8}{x}=a\cdot\dfrac{1}{log_{2}(8)}\\\\\\log_{8}(x)=a\cdot\dfrac{1}{3}\\\\\\\boxed{\boxed{log_{8}(x)=\dfrac{a}{3}}}$