Question 3: Expand the following using laws of logarithms:
\((iv)\) \(\quad \)\(log\left(\frac{xy}{z}\right)^{\frac{1}{9}}\)
Solution:
\[
\begin{align*}
&=\log\left(\frac{xy}{z}\right)^{\large{\frac{1}{9}}}\\
&=\frac{1}{9}\log\left(\frac{xy}{z}\right)\\
&=\frac{1}{9}[\log xy-\log z]\\
&=\frac{1}{9}[\log x+\log y-\log z]\\
\end{align*}
\]