Question
If $${\log _2}\left[ {{{\log }_3}\left( {{{\log }_2}x} \right)} \right] = 1,$$ Â Â then x is equal to = ?
Answer: Option D
$$\eqalign{
& {{\log }_2}\left[ {{\text{ }}{{\log }_3}\left( {{\text{ }}{{\log }_2}x} \right)} \right] = 1 \cr
& \Rightarrow {\log _3}\left( {{{\log }_2}x} \right) = {2^1} = 2 \cr
& \Rightarrow {\log _2}x = {3^2} = 9 \cr
& \Rightarrow x = {2^9} = 512 \cr} $$
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$$\eqalign{
& {{\log }_2}\left[ {{\text{ }}{{\log }_3}\left( {{\text{ }}{{\log }_2}x} \right)} \right] = 1 \cr
& \Rightarrow {\log _3}\left( {{{\log }_2}x} \right) = {2^1} = 2 \cr
& \Rightarrow {\log _2}x = {3^2} = 9 \cr
& \Rightarrow x = {2^9} = 512 \cr} $$
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