$x^{log_2 x} = 2^4$
Solve for x.
How to do this?
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5Take $\log_2$ on both sides, for starters. – Sarvesh Ravichandran Iyer Jan 19 '21 at 09:30
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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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