Q. The value of $\log_{2}{\log_{3}{\ldots\log_{100}100^{99^{98^{.^{.^{2^{1}}}}}}}}$ is equal to
A) 0
B) 1
C) 2
D) $100!$
Explanation
(b)
Let $S = \log_{2}{\log_{3}{\ldots\log_{99}{\log_{100}100^{99^{98^{.^{.^{2^{1}}}}}}}}}$
$= \log_{2}{\log_{3}{\ldots\log_{99}{99^{98^{.^{.^{2^{1}}}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack\because\log_{a}{a = 1}\rbrack}}}$
$= \log_{2}{2^{1} = 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.