Answer
$\log_3 x$ + $\frac{1}{2}$$\log_3 y$
Work Step by Step
$Expand$ $the$ $expression$:
$\log_3 (x \sqrt{y})$
Rewrite the root for y
$\log_3 (xy^\frac{1}{2})$
Apply the First Law of Logarithms
$\log_3 (x\times y^\frac{1}{2})$ = $\log_3 x$ + $\log_3 y^\frac{1}{2}$
Apply the Third Law of Logarithms for $\log_3 y^\frac{1}{2}$
$\log_3 y^\frac{1}{2}$ = $\frac{1}{2}$$\log_3 y$
$\log_3 x$ + $\log_3 y^\frac{1}{2}$ = $\log_3 x$ + $\frac{1}{2}$$\log_3 y$
