Question

Evaluate:
${\log }_5\frac{\sqrt[4]{425}}{625}$

Answer 1

A] $lo{g}_5\frac{\sqrt[4]{425}}{625}$

= $lo{g}_5\frac{\sqrt[4]{45^2}}{(5{)}^4}=lo{g}_5\frac{(5{)}^{2/4}}{5^4}=lo{g}_5\frac{5^{1/2}}{5^4}$

= $lo{g}_5{5}^{1/2-4}$

= $lo{g}_5{5}^{-7/2}$

= $-\frac{7}{2}\times 1=-\frac{7}{2}$