Question

Determine the value of the following
${\log }_{\frac{2}{3}}\left(\frac{8}{27}\right)$

Answer 1

$lo{g}_{\frac{2}{3}}\left(\frac{8}{27}\right)$

$=lo{g}_{\frac{2}{3}}(\frac{2}{3}{)}^3$

$=3lo{g}_{\frac{2}{3}}\frac{2}{3}$ $[\because log{a}^m=mloga]$

$=3\left(1\right)$ $[\because lo{g}_{x}x=1]$

$\therefore lo{g}_{\frac{2}{3}}\left(\frac{8}{27}\right)=3$