Answer
$\displaystyle \ln\frac{x^{3}y^{5}}{z^{6}}$
Work Step by Step
$ 3\ln x+5\ln y-6\ln z=\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\ln x^{3}+\ln y^{5}-\ln z^{6}=\quad $...apply the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
$=\ln(x^{3}\cdot y^{5})-\ln z^{6}=\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \ln\frac{x^{3}y^{5}}{z^{6}}$
