Question

Evaluate: ${\log }_{\frac{1}{8}}\frac{1}{1024}$

Answer 1

given, ${\log }_{\frac{1}{2^3}}\frac{1}{2^{10}}$

$={\log }_{2^{-3}}{2}^{-10}$

$=\frac{-10}{-3}{\log }_{10}10$ using ${\log }_{a^n}{a}^m=\frac{m}{n}{\log }_{a}a$

$=\frac{10}{3}$ since ${\log }_{a}a=1$