Answer
$\displaystyle \frac{1}{2}\log_{b}x+3\log_{b}y-3\log_{b}z $
Work Step by Step
$\displaystyle \log_{b}\frac{\sqrt{x}y^{3}}{z^{3}}=\log_{b}\frac{x^{1/2}y^{3}}{z^{3}}$
$\quad $..apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\log_{b}x^{1/2}+\log_{b}y^{3}-\log_{b}z^{3}$
$\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\displaystyle \frac{1}{2}\log_{b}x+3\log_{b}y-3\log_{b}z $
