Answer
$\frac{1}{2}\log x+\frac{1}{4}\log y+\frac{1}{8}\log z$
Work Step by Step
$\log\sqrt{x\sqrt{y\sqrt{z}}}=\log(x\sqrt{y\sqrt{z}})^{1/2}=\frac{1}{2}\log(x\sqrt{y\sqrt{z}})=\frac{1}{2}(\log x+\log\sqrt{y\sqrt{z}})=\frac{1}{2}[\log x+\frac{1}{2}\log(y\sqrt{z})]=\frac{1}{2}[\log x+\frac{1}{2}(\log y+\frac{1}{2}\log z)]=\frac{1}{2}\log x+\frac{1}{4}\log y+\frac{1}{8}\log z$
