Q. If $\log_{\sqrt{3}}{5 = a}$ and $\log_{\sqrt{3}}{2 = b}$, then $\log_{\sqrt{3}}300$ is equal to
A) $2(a + b)$
B) $2(a + b + 1)$
C) $2(a + b + 2)$
D) $a + b + 4$
Explanation
(b)
$\log_{\sqrt{3}}{300 = \log_{\sqrt{3}}{3 + \log_{\sqrt{3}}100}}$
$= 2\log_{\sqrt{3}}{\sqrt{3} + 2\log_{\sqrt{3}}{5 + 2\log_{\sqrt{3}}2}}$
$= 2(1 + a + b)\ \ \ \ \ \ \ \lbrack\because\log_{\sqrt{b}}{5 = a,\log_{\sqrt{b}}{2 = b}}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.