Question

Show that ${\left(2\sqrt{2}\right)}^{-2/3}=\frac{1}{2}.$ can be written as ${\log }_{2\sqrt{2}}2=-\frac{2}{3}$

Answer 1

Given equation

${\left(2\sqrt{2}\right)}^{-2/3}=\frac{1}{2}.$

Taking log with base $2\sqrt{2}$
${\log }_{2\sqrt{2}}\left(\frac{1}{2}\right)=-\frac{2}{3}$