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Question Number 139600 by rexford last updated on 29/Apr/21

	Answered by mr W last updated on 29/Apr/21
	$2^x =4x e^(xln 2) =4x xe^(−xln 2) =(1/4) (−xln 2)e^(−xln 2) =−((ln 2)/4) −xln 2=W(−((ln 2)/4)) ⇒x=−((W(−((ln 2)/4)))/(ln 2))= { ((−((−0.21481112)/(ln 2))=0.309906)),((−((−2.772589)/(ln 2))=4)) :}$
	$2^{x} = 4 x$ $e^{x \ln 2} = 4 x$ ${x e}^{- x \ln 2} = \frac{1}{4}$ $(- x \ln 2) e^{- x \ln 2} = - \frac{\ln 2}{4}$ $- x \ln 2 = W (- \frac{\ln 2}{4})$ $\Rightarrow x = - \frac{W (- \frac{\ln 2}{4})}{\ln 2} = {\begin{cases} - \frac{- 0.21481112}{\ln 2} = 0.309906 \\ - \frac{- 2.772589}{\ln 2} = 4 \end{cases}$
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