Expand the Logarithmic Expression log base 4 of fifth root of 4

$\log_{4} (\sqrt[5]{4})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{4}$ as $4^{\frac{1}{5}}$ .

$\log_{4} (4^{\frac{1}{5}})$

Expand $\log_{4} (4^{\frac{1}{5}})$ by moving $\frac{1}{5}$ outside the logarithm.

$\frac{1}{5} \log_{4} (4)$

Logarithm base $4$ of $4$ is $1$ .

$\frac{1}{5} \cdot 1$

Multiply $\frac{1}{5}$ by $1$ .

$\frac{1}{5}$