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