Question

The value of $\sqrt{{\left({\log }_{0.5}4\right)}^2}$ is equal to

Answer 1

$t=\sqrt{{\left({\log }_{0.5}4\right)}^2}=\sqrt{{(-{\log }_{2}4)}^2}=\sqrt{{\left({\log }_{2}4\right)}^2}$
$\Rightarrow t={\log }_{2}4={\log }_2{2}^2=2,[\because {\log }_{a}a=1]$
Answer: 2