We will use the following two properties of the logarithmic function
[tex]\begin{gathered} \ln (\frac{M}{N})=\ln M-\ln N \\ \text{and} \\ \ln (M^a)=a\ln M \end{gathered}[/tex]Therefore, given
[tex]\ln (\frac{x^3}{e^2})[/tex]Simplify as shown below
[tex]\begin{gathered} \ln (\frac{x^3}{e^2})=\ln (x^3)-\ln (e^2) \\ =3\ln (x)-2\ln (e);\ln (e)=1 \\ =3\ln (x)-2\cdot1 \\ =3\ln (x)-2 \\ \Rightarrow\ln (\frac{x^3}{e^2})=3\ln (x)-2 \end{gathered}[/tex]The answer is 3ln(x)-2
