Question 8: Expand the following using laws of logarithms:
\((iii)\) \(\quad\) \(\log\sqrt{8x^{3}}\)
Solution:
\[
\begin{align*}
&=\log\sqrt{8x^{3}}\\
&=\log\left( 2^{3} x^{3}\right)^{\frac{1}{2}}\\
&=\frac{1}{2}\log\left( 2^{3} x^{3}\right)\\
&=\frac{1}{2}\left[\log 2^{3} +\log x^{3}\right]\\
&=\frac{1}{2}[ 3\log 2 +3\log x]\\
&=\frac{3}{2}[\log 2 +\log x]\\
\end{align*}
\]