\begin{itemize}
\item $\ln 4= \ln \big(2^2\big) = 2\ln 2 $.

\item $\ln 36 = \ln (4\times 9) = \ln\left(2^2 \times 3^2 \right) = 2\ln 2 + 2\ln 3 $.

\item $\ln \dfrac{2}{27} = \ln\left(2\times 3^{ - 3}\right) = \ln 2- 3\ln 3$.

\item $ \ln \sqrt{6} = \ln\left((2\times 3)^{\frac{1}{2}}\right) = \dfrac{1}{2}\ln (2\times 3) = \dfrac{1}{2} (\ln 2 + \ln 3)$.

\item $ \ln \dfrac{9}{8} = \ln 3^2 - \ln (2^3) = 2\ln 3 - 3\ln 2 $.

\item $ \ln\left(3\nep ^{5}\right) = \ln 3 + 5\underbrace{\ln\nep}_1 = \ln 3 + 5$.
\end{itemize}
