Expand the Logarithmic Expression log base 3 of square root of 3

$\log_{3} (\sqrt{3})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\log_{3} (3^{\frac{1}{2}})$

Expand $\log_{3} (3^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{3} (3)$

Logarithm base $3$ of $3$ is $1$ .

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

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

$\frac{1}{2}$