Question

Calcule log de 3 na base $\sqrt[3]{9}$

Answer 1

Resposta:

$\log_\sqrt[3]{9} }3=x\\ \\ (\sqrt[3]{9} )^x=3\\ \\ (9^{1\over3})^x=3\\ \\ (3^{2.{1\over3}})^x=3\\ \\ 3^{2\over3}^x=3^1\\ \\ {2\over3}x=1\\ \\ 2x=3\\ \\ x={3\over2}\\ \\ ou~~~x= 1,5$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\Large\boxed{\begin{array}{I}\tt \mathsf{log_{\sqrt[3]{9}}\:3 = log_{3^\frac{2}{3}}\:3}\\\\\mathsf{log_{3^\frac{2}{3}}\:3 = \dfrac{3}{2}\:log_3\:3}\\\\\mathsf{log_{\sqrt[3]{9}}\:3 = \dfrac{3}{2}} \end{array}}}$