Question

Simplify the following expressions.
$lo{g}_{1/4}(lo{g}_{2}3\cdot lo{g}_{3}4)$

Answer 1

${\log }_{1/4}\left({\log }_{2}3.{\log }_{3}4\right)$

$={\log }_{1/4}\left({\log }_{2}4\right)$

$={\log }_{1/4}2$

$=-{\log }_{4}2$

$=\frac{-1}{2}$