Question 2: Write the following as a single logarithm:
\((i)\) \(\quad\) \(\frac{1}{2} \log\ 25+2\log\ 3 \)
Solution:
\[
\begin{align*}
&=\frac{1}{2}\log 25+2\log 3\\
&=\frac{1}{2}\log 5^{2} +\log 3^{2}\\
&=\frac{2}{2}\log 5 +\log 9\\
&=\log 5 +\log 9\\
&=\log( 5\times 9)\\
&=\log( 45)\\
\end{align*}
\]