Question

The value of ${\log }_{\sqrt{3}}81$ is

• A. $4$
• B. $8$
• C. $12$
• D. none of these

Answer 1

Answer: (B)

$8$

Now,

${\log }_{\sqrt{3}}81$

$={\log }_{\sqrt{3}}{3}^4$

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

$=8{\log }_{\sqrt{3}}\left(\sqrt{3}\right)$

$=8$. [ Since ${\log }_{a}a=1$ for $a>0$]