Question # 01: Without using calculator, evaluate the following:
\((v)\) \(\quad\)\( \frac{1}{3} \log_4\ 64+2\log_5\ 25\)
Solution:
\[
\begin{align*}
&=\frac{1}{3}\log_{4} 64+\log_{5} 25\\
&=\frac{1}{3}\log_{4}( 4)^{3} +\log_{5}( 5)^{2}\\
&=\frac{3}{3}\log_{4} 4+2\log_{5} 5\\
&=1( 1) +2( 1)\\
&=1+2\\
&=3\\
\end{align*}
\]