Question

Find the value of ${\log }_{\sqrt{3}}81$.

Answer 1

$lo{g}_{\left(\sqrt{3}\right)}^{\left(81\right)}$

$=lo{g}_{\left(\sqrt{3}\right)}^{3^4}$

$=lo{g}_{\sqrt{3}}^{(\sqrt{3}{)}^8}$

$=8lo{g}_{\sqrt{3}}^{\sqrt{3}}$

$=8[\because lo{g}_a^a=1$ for $a>1]$.