Answer
$$\ln \left ( \frac{\sqrt{x}}{y^3(z-2)} \right )$$
Work Step by Step
We simplify as follows:
$$\frac{1}{2} \ln x -3 \ln y - \ln (z-2) = \frac{1}{2} \ln x - ( 3 \ln y + \ln (z-2)) \\ = \ln x ^{\frac{1}{2}} - (\ln y^3+\ln (z-2))= \ln \sqrt{x} - \ln y^3(z-2) \\= \ln \left ( \frac{\sqrt{x}}{y^3(z-2)} \right )$$
