Question

Which one of the two is greater ?
${\log }_{4}5$ or ${\log }_{\frac{1}{16}}\left(\frac{1}{25}\right)$

• A. ${\log }_{4}5.$
• B. ${\log }_{\frac{1}{16}}\left(\frac{1}{25}\right)$
• C. Equal
• D. can't say

Answer 1

The correct option is C Equal

${\log }_{\frac{1}{16}}\frac{1}{25}={\log }_{4^{-2}}{5}^{-2}=\left(\frac{-2}{-2}\right){\log }_{4}5[\because {\log }_{a^n}{b}^m=\frac{m}{n}{\log }_{a}b]={\log }_{4}5.$

Hence ${\log }_{4}5$ and ${\log }_{\frac{1}{16}}\frac{1}{25}$ are equal.