Question

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

Answer 1

$lo{g}_5\frac{\sqrt[4]{425}}{625}$ $[log\frac{a}{b}=loga-logb]$

$=lo{g}_5\sqrt[4]{425}-lo{g}_{5}625$

$\Rightarrow lo{g}_5{25}^{1/4}-lo{g}_5{25}^2$

$=\frac{1}{4}lo{g}_{5}25-2lo{g}_{5}25$ $[lo{g}_{5}25=2]$

$\Rightarrow \frac{1}{4}\times 2-2\times 2$

$\Rightarrow \frac{1}{2}-4=\frac{-3}{2}$