Answer
$\displaystyle \ln\frac{x^{4}y^{7}}{z^{3}}$
Work Step by Step
$ 4\ln x+7\ln y-3\ln z=\quad $
...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\ln x^{4}+\ln y^{7}-\ln z^{3} \quad $
...apply the Product Rule: $\quad \log_{b}(MN)=\log_{b}\mathrm{M}+\log_{b}\mathrm{N}$
$=\ln(x^{4}\cdot y^{7})-\ln z^{3} \quad $
...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\displaystyle \ln\frac{x^{4}y^{7}}{z^{3}}$
