Answer
$\ln x+\frac{1}{2}\ln y-\frac{1}{2}\ln z$
Work Step by Step
$\ln(x\sqrt{\frac{y}{z}})=\ln x+\ln((\frac{y}{z})^{1/2})=\ln x+\frac{1}{2}\ln(\frac{y}{z})=\ln x+\frac{1}{2}(\ln y-\ln z)=\ln x+\frac{1}{2}\ln y-\frac{1}{2}\ln z$
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