Answer
$\frac{1}{2} \log _b {x} + 3\log _b {y}-3 \log_b{z} $.
Work Step by Step
The given expression is
$=\log_b{\left ( \frac{\sqrt x y^3}{z^3} \right )}$
Use the quotient rule.
$\log_b {\sqrt xy^3}- \log_b{z^3}$
Use the product rule.
$\log _b \sqrt x + \log _b {y^3}- \log_b{z^3} $
$\log _b x ^{\frac{1}{2}} + \log _b {y^3}- \log_b{z^3} $
Use the power rule.
$\frac{1}{2} \log _b {x} + 3\log _b {y}-3 \log_b{z} $.
