Question

Evaluate: ${\log }_5\left(\frac{\sqrt[4]{425}}{625}\right)$.

Answer 1

Now,

${\log }_5\left(\frac{\sqrt[4]{425}}{625}\right)$

$={\log }_5\left(\frac{\sqrt[4]{425}}{{25}^2}\right)$

$={\log }_5\left(\frac{\sqrt[4]{45^2}}{5^4}\right)$

$={\log }_5\left(\frac{5^{\frac{1}{2}}}{5^4}\right)$

$={\log }_5\left(5^{\frac{1}{2}-4}\right)$

$={\log }_5\left(5^{-\frac{7}{2}}\right)$

$=-\frac{7}{2}$.