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

$\log_{5} (\sqrt{5})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\log_{5} (5^{\frac{1}{2}})$

Expand $\log_{5} (5^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{5} (5)$

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

$\frac{1}{2} \cdot 1$

Multiply $\frac{1}{2}$ by $1$ .

$\frac{1}{2}$