Question

log de raiz quinta de 16 na base raiz cubica de 2

Answer 1

Explicação passo-a-passo:

$\sf log_{\sqrt[3]{2}}~\sqrt[5]{16}=x$

$\sf (\sqrt[3]{2})^x=\sqrt[5]{16}$

$\sf (2^{\frac{1}{3}})^x=\sqrt[5]{2^4}$

$\sf 2^{\frac{x}{3}}=2^{\frac{4}{5}}$

Igualando os expoentes:

$\sf \dfrac{x}{3}=\dfrac{4}{5}$

$\sf 5x=3\cdot4$

$\sf 5x=12$

$\sf \red{x=\dfrac{12}{5}}$