Question

Evaluate: ${\log }_{\sqrt{3}}243$

Answer 1

${\log }_{\sqrt{3}}243$

$={\log }_{3^{\frac{1}{2}}}243$

$=\frac{1}{\frac{1}{2}}{\log }_{3}243$

$=2{\log }_{3}243$

$=2{\log }_3{3}^5$

$=2\times 5{\log }_{3}3$ using $\log a^m=m\log a$

$=10$ using ${\log }_{a}a=1$