If $${\log _2}\left[ {{{\log }_3}\left( {{{\log }_2}x} \right)} \right] = 1,$$     then x is equal to = ?

A. 0

B. 12

C. 128

D. 512

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & {{\log }_2}\left[ {{\text{ }}{{\log }_3}\left( {{\text{ }}{{\log }_2}x} \right)} \right] = 1 \cr & \Rightarrow {\log _3}\left( {{{\log }_2}x} \right) = {2^1} = 2 \cr & \Rightarrow {\log _2}x = {3^2} = 9 \cr & \Rightarrow x = {2^9} = 512 \cr} $$