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$x^{log_2 x} = 2^4$

Solve for x.

How to do this?

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    $\begingroup$ Take $\log_2$ on both sides, for starters. $\endgroup$ – Teresa Lisbon Jan 19 at 9:30
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By some easy algebraic computations, we get $x^{\log_2x}=2^{\log_2(x^{\log_2x})}=2^{\log_2x \times \log_2x}=2^{\log_2^2x}$.
$\Rightarrow \log_2^2x = 4$
$\Rightarrow \log_2x = \pm 2$
$\Rightarrow x_1 = 2^2 = 4$ and $x_2 = 2^{-2} = \frac{1}{4}$

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