Solve: ${log}_{2} [{log}_{3} ({log}_{2} x)] = 1$

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Solution

Let ${log}_{2} [{log}_{3} ({log}_{2} x)] = 1$
$\Rightarrow {log}_{3} ({log}_{2} x) = 2^{1} = 2$
$\Rightarrow {log}_{2} x = 3^{2}$
$\Rightarrow {log}_{2} x = 9$
$\Rightarrow x = 2^{9}$
$\Rightarrow x = 512$
$∴ x = 512$

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