Answer
$\frac{1}{3} \log _b {x} + 4\log _b {y}-5 \log_b{z} $.
Work Step by Step
The given expression is
$=\log_b{\left ( \frac{\sqrt[3] x y^4}{z^5} \right )}$
Use the quotient rule.
$\log_b {\sqrt[3] xy^4}- \log_b{z^5}$
Use the product rule.
$\log _b \sqrt[3] x + \log _b {y^4}- \log_b{z^5} $
$\log _b x ^{\frac{1}{3}} + \log _b {y^4}- \log_b{z^5} $
Use the power rule.
$\frac{1}{3} \log _b {x} + 4\log _b {y}-5 \log_b{z} $.
