Question # 01: Without using calculator, evaluate the following:
\((ii)\) \(\quad\) \(\text{log}_2\ 64 + \text{log}_2\ 2 \)
Solution:
\[
\begin{align*}
&=\log_{2} 64+\log_{2} 2\\
&=\log_{2}( 64\times 2)\\
&=\log_{2}( 2\times 2\times 2\times 2\times 2\times 2\times 2)\\
&=\log_{2}\left( 2^{7}\right)\\
&=7\log_{2} 2\\
&=7( 1)\\
&=7\\
\end{align*}
\]
——– Alternate Method ——–
\[
\begin{align*}
&=\text{log}_{2} 64+\text{log}_{2} 2\\
&=\text{log}_{2} 64+1\\
&=\text{log}_{2}( 2\times 2\times 2\times 2\times 2\times 2) +1\\
&=\text{log}_{2}\left( 2^{6}\right) +1\\
&=6\text{log}_{2}( 2) +1\\
&=6( 1) +1\\
&=6+1\\
&=7
\end{align*}
\]