Expand the Logarithmic Expression log base 2 of square root of 2

$\log_{2} (\sqrt{2})$

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

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

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

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

Logarithm base $2$ of $2$ is $1$ .

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

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

$\frac{1}{2}$