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