x^2 =4^x x=?


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Question Number 170117 by mathlove last updated on 16/May/22

$x^{2} = 4^{x} x = ?$
Commented by mathlove last updated on 16/May/22

$x^{2} = 4^{x}$ $s o l v e t h i s b e f o r I m f a l l$
	Answered by mr W last updated on 16/May/22

	$x^{2} = 2^{2 x}$ $x = \pm 2^{x}$ $x = \pm e^{x \ln 2}$ $(- x \ln 2) e^{- x \ln 2} = \pm \ln 2$ $- x \ln 2 = W (\pm \ln 2)$ $f o r x \in R :$ $\Rightarrow x = - \frac{W (\ln 2)}{\ln 2} \approx - \frac{0.44443609}{\ln 2} = - 0.641186$
	Commented by mathlove last updated on 17/May/22

	$t h a n k s$
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