solve: 2^x^2 =x^(2x)


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Question Number 172021 by Mikenice last updated on 23/Jun/22

$s o l v e :$ $2^{x^{2}} = x^{2 x}$
	Answered by puissant last updated on 23/Jun/22

	$\Rightarrow x^{2} l n 2 = 2 x l n x$ $\Rightarrow x l n 2 = 2 l n x$ $\Rightarrow \frac{l n x}{x} = \frac{l n 2}{2} \Rightarrow x = 2$
	Commented by mr W last updated on 23/Jun/22

	$\frac{l n x}{x} = \frac{l n 2}{2} = \frac{2 \times \ln 2}{2 \times 2} = \frac{\ln 4}{4}$ $\Rightarrow x = 2, x = 4$ $f r o m \frac{a}{b} = \frac{c}{d} w e g e t n o t o n l y$ $a = c, b = d . b u t g e n e r a l l y$ $a = k c, b = k d .$
	Commented by Tawa11 last updated on 25/Jun/22

	$Great sir$
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