Expand the Logarithmic Expression log base 3 of square root of 27

$\log_{3} (\sqrt{27})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{27}$ as $27^{\frac{1}{2}}$ .

$\log_{3} (27^{\frac{1}{2}})$

Expand $\log_{3} (27^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{3} (27)$

Logarithm base $3$ of $27$ is $3$ .

$\frac{1}{2} \cdot 3$

Combine $\frac{1}{2}$ and $3$ .

$\frac{3}{2}$