College Algebra, Chapter 5, 5.3, Section 5.3, Problem 32

Expand the expression $\displaystyle \ln \sqrt[3]{3r^2 s}$, using Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\ln \sqrt[3]{3r^2 s} =& \ln (3r^2 s)^{\frac{1}{3}}
&& \text{Exponential Form}
\\
\\
\ln \sqrt[3]{3r^2 s} =& \frac{1}{3} \ln (3r^2 s)
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
\ln \sqrt[3]{3r^2 s} =& \frac{1}{3} (\ln 3 + \ln r^2 + \ln s)
&& \text{Law of Logarithm } \ln (AB) = \ln A + \ln B
\\
\\
\ln \sqrt[3]{3r^2 s} =& \frac{1}{3} (\ln 3 + 2 \ln r + \ln s)
&& \text{Law of Logarithm } \ln A^C = C \ln A


\end{aligned}
\end{equation}
$