Question

determine o valor de:
​

Answer 1

$\boxed{\log_b{a}=x\iff b^x=a}$

a)

$\log_{\sqrt{2}}{4}=x\iff \left(\sqrt{2}\right)^x=4\\\\ \Longrightarrow 2^{\frac{x}{2}}=2^2\Longrightarrow\dfrac{x}{2}=2\ \therefore\ \boxed{x=4}$

b)

$\log_{\sqrt[3]{4}}{2}=y\iff\left(\sqrt[3]{4}\right)^y=2\\\\ \Longrightarrow2^{\frac{2y}{3}}=2^1\Longrightarrow\dfrac{2y}{3}=1\ \therefore\ \boxed{y=\dfrac{3}{2}}$

c)

$\log_7{\sqrt[5]{49}}=z\iff7^z=\sqrt[5]{7^2}\\\\ \Longrightarrow7^z=7^{\frac{2}{5}}\ \therefore\ \boxed{z=\dfrac{2}{5}}$