Answer
$log _{b} 0.5=-2
$
Not possible, log Values
Cannot be Negative.
Work Step by Step
\[
\begin{array}{l}
\text { Given log }_{b} 20=11 \text { , log }_{b}40=13 \\
\log _{b} 0.5=? \\Using \log _{b}\left(\frac{m}{n}\right)=\log _{b} m-\log _{b} n
Put \ m=20, n=40\
\end{array}
\]
$\therefore \log _{b}\left(\frac{20}{40}\right)=\log _{b} 20-\log _{b} 40$
\[
\Rightarrow \log _{b} 0.5=11-13
\]
\[
\therefore \log _{b} 0.5=-2
\]
Not possible, log Values
Cannot be Negative.