Question

Questao de logaritimos, me ajudem

Answer 1

Olá!

O primeiro item:

$\displaystyle \log_{\sqrt[3]{4}}\sqrt{2}=x\Leftrightarrow (\sqrt[3]{4})^x=\sqrt{2} \Leftrightarrow (4^{\frac{1}{3}})^x=2^{\frac{1}{2}}\Leftrightarrow \\ \\ \Leftrightarrow (2^{2\cdot \frac{1}{3}})^x=2^{\frac{1}{2}} \Leftrightarrow 2^{\frac{2x}{3}} =2^{\frac{1}{2}}\Leftrightarrow \dfrac{2x}{3}=\dfrac{1}{2} \Leftrightarrow \\ \\ \\ \Leftrightarrow x = \dfrac{3}{4}.$


O segundo item:


$\log_{m^2}\sqrt[3]{m}=x\Leftrightarrow (m^2)^x=\sqrt[3]{m}\Leftrightarrow 2x = \dfrac{1}{3}\Leftrightarrow x=\dfrac{1}{6}.$


Bons estudos!