If $4^{{log}_{2} 2 x} = 36$ , then find x.

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Solution

$4^{{log}_{2} 2 x} = 36$ and $x > 0$
$\Rightarrow (2)^{2 {log}_{2} 2 x} = 36$
$\Rightarrow (2)^{{log}_{2} {2 x}^{2}} = 36$
$\Rightarrow (2 x)^{2} = 36$
$\Rightarrow (2 x)^{2} - (6)^{2} = 0$
$\Rightarrow (2 x - 6) (2 x + 6) = 0$
$\Rightarrow x = 3, - 3$
$\Rightarrow x \neq - 3, x = 3$

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