4^x = 2x find x


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Question Number 6045 by sanusihammed last updated on 10/Jun/16

$4^{x} = 2 x$ $f i n d x$
Commented by Yozzii last updated on 10/Jun/16

$4^{x} = 2 x$ $2^{2 x} = 2 x$ $- 1 = - 2 x (2^{- 2 x})$ $- 1 = - 2 {x e}^{l n 2^{- 2 x}}$ $- 1 = - 2 {x e}^{- 2 x l n 2}$ $- l n 2 = (- 2 x l n 2) e^{- 2 x l n 2}$ $\Rightarrow W (- l n 2) = - 2 x l n 2$ $x = - \frac{W (- l n 2)}{2 l n 2} (F o l l o w i n g {P r a k a s h}^{'} s e x a m p l e)$
	Answered by Yozzii last updated on 11/Jun/16

	$x = - \frac{W (- l n 2)}{2 l n 2}$
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