Expand the Logarithmic Expression log base 5 of cube root of 5

$\log_{5} (\sqrt[3]{5})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5}$ as $5^{\frac{1}{3}}$ .

$\log_{5} (5^{\frac{1}{3}})$

Expand $\log_{5} (5^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{5} (5)$

Logarithm base $5$ of $5$ is $1$ .

$\frac{1}{3} \cdot 1$

Multiply $\frac{1}{3}$ by $1$ .

$\frac{1}{3}$