Examveda

# 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

### Solution(By Examveda Team)

\eqalign{ & \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}
Related Questions on Logarithm

If ax = by, then:

A. $$\log \frac{a}{b} = \frac{x}{y}$$

B. $$\frac{{\log a}}{{\log b}} = \frac{x}{y}$$

C. $$\frac{{\log a}}{{\log b}} = \frac{y}{x}$$

D. None of these