Question # 01: Without using calculator, evaluate the following:
\((iii)\) \(\quad\) \(\frac{1}{3} log_3\ 8 -log_3\ 18\)
Solution:
\[
\begin{align*}
&=\frac{1}{3}\log_{3} 8-\log_{3} 18\\
&=\frac{1}{3}\log_{3} 2^{3} -\log_{3} 18\\
&=\frac{3}{3}\log_{3} 2 -\log_{3} 18\\
&=\log_{3} 2 -\log_{3} 18\\
&=\log_{3}\left(\frac{2}{18}\right)\\
&=\log_{3}\left(\frac{1}{9}\right)\\
&=\log_{3}\left(\frac{1}{3^{2}}\right)\\
&=\log_{3} 3^{-2}\\
&=-2\log_{3} 3\\
&=-2( 1)\\
&=-2
\end{align*}
\]