Question 2: Write the following as a single logarithm:
\((vi)\) \(\quad\) \(2\ln\ a +3\ln\ b-4\ln\ c \)
Solution:
\[
\begin{align*}
&=2\ln a+3\ln b-4\ln c\\
&=\ln a^{2} +\ln b^{3} -\ln c^{4}\\
&=\ln a^{2} +\ln\frac{b^{3}}{c^{4}}\\
&=\ln\frac{a^{2} b^{3}}{c^{4}}
\end{align*}
\]