Find the Exact Value log base 3 of square root of 27

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

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\log_{3} (\sqrt{9 (3)})$

Rewrite $9$ as $3^{2}$ .

$\log_{3} (\sqrt{3^{2} \cdot 3})$

Pull terms out from under the radical.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.5$