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

$\log_{4} (\sqrt{4})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4}$ as $4^{\frac{1}{2}}$ .

$\log_{4} (4^{\frac{1}{2}})$

Expand $\log_{4} (4^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{4} (4)$

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

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

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

$\frac{1}{2}$