Question

qual valor de log8 3√16 é:

Answer 1

Resposta:

$\text{Leia abaixo}$

Explicação passo-a-passo:

$\text{log}_8\: \sqrt[3]{16}$

$\text{log}_8\: 16^{\frac{1}{3}}$

$\text{log}_8\: 2^{\frac{4}{3}}$

$8^x = 2^{\frac{4}{3}}$

$2^{3x} = 2^{\frac{4}{3}}$

$3x = \dfrac{4}{3}$

$\boxed{\boxed{x = \dfrac{4}{9}}}$

Answer 2

Explicação passo-a-passo:

$\sf log_{8}~\sqrt[3]{16}$

$\sf =log_{2^3}~\sqrt[3]{2^4}$

$\sf =log_{2^3}~2^{\frac{4}{3}}$

Lembre-se que $\sf log_{b^m}~a^n=\dfrac{n}{m}\cdot log_{b}~a$

Assim:

$\sf log_{2^3}~2^{\frac{4}{3}}$

$\sf =\dfrac{\frac{4}{3}}{3}\cdot log_{2}~2$

$\sf =\dfrac{4}{3}\cdot\dfrac{1}{3}\cdot1$

$\sf =\red{\dfrac{4}{9}}$