Question

If ${\log }_{125}p=\frac{1}{6}$, then find the value of $p$.

Answer 1

$lo{g}_{125}p=\frac{1}{6}$

This can be written as $p=(125{)}^{\frac{1}{6}}$

$p=(125{)}^{\frac{1}{6}}$

$=(5{)}^{3\times \frac{1}{6}}$

$=(5{)}^{\frac{1}{2}}$

$=\sqrt{5}$

$\therefore p=\sqrt{5}$.