Chapter 3 - Section 3.3 - Properties of Logarithms - Exercise Set - Page 475: 57

$\displaystyle \ln(\frac{x^{3}}{\sqrt[3]{y}})$

$ 3\displaystyle \ln x-\frac{1}{3}\ln y=\quad $...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$ $=\ln x^{3}-\ln y^{1/3}\quad $...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$ $=\displaystyle \ln(\frac{x^{3}}{y^{1/3}})$