Answer
$log _{b} 5=2$
Work Step by Step
Given $log _{b} 100=4, \log _{b} 500=6$
\[
\begin{array}{c}
\log _{b} 5=? \\
\text { using } \log _{b}\left(\frac{m}{n}\right)=\log _{b} m-\log _{b} n
\end{array}
\]
Put $m=500, n=100$
\[
\therefore \log _{b}\left(\frac{500}{100}\right)=\log _{b} 500-\log _{b} 100
\]
\[
\begin{array}{l}
\Rightarrow \log _{b} 5=6-4 \\
\therefore \log _{b} 5=2
\end{array}
\]
