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1. If $\log_{2} [\log_{3} (\log_{2} x)] = 1,$ then x is equal to = ?

A. 0

B. 12

C. 128

D. 512

Solution:

\begin{aligned} \log_{2} [\log_{3} (\log_{2} x)] = 1 \\ \Rightarrow \log_{3} (\log_{2} x) = 2^{1} = 2 \\ \Rightarrow \log_{2} x = 3^{2} = 9 \\ \Rightarrow x = 2^{9} = 512 \end{aligned}

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