Question

$lo{g}_{\frac{1}{2}}8=?$

Answer 1

${\log }_{1/2}8$

$={\log }_{2^{-1}}8$

$=-{\log }_2\left(2^3\right)(\because {\log }_{a^b}c=\frac{1}{b}{\log }_{a}c)$

$=-3{\log }_{2}2(\because {\log }_a\left(b^c\right)=c{\log }_{a}b)$

$=-3(\because {\log }_{a}a=1)$

Hence the correct answer is $-3$.