Question

Evaluate:\log_{\frac{1}{100}}{\dfrac{1}{10000}}

Answer 1

Let $a={\log }_{\frac{1}{100}}\frac{1}{10000}$

$={\log }_{{10}^{-2}}{10}^{-4}$

We know that, ${\log }_{a^n}{a}^m=\frac{m}{n}{\log }_{a}a$

$a=\frac{-4}{-2}{\log }_{10}10$

We know that, ${\log }_{a}a=1$

$a=2$

$\therefore {\log }_{\frac{1}{100}}\frac{1}{10000}=2$