Question

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

Answer 1

$\sqrt{{\left({\log }_{0.5}4\right)}^2}$
$=\sqrt{{\left({\log }_{1/2}{2}^2\right)}^2}$
$=\sqrt{{\left({\log }_{2^{-1}}{2}^2\right)}^2}$
$=\sqrt{{\left(\frac{2}{-1}{\log }_{2}2\right)}^2}$
$=\sqrt{4{\left({\log }_{2}2\right)}^2}$
$=\sqrt{4}$
$=2$