2^x + 2x = 8 find the value of x


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Question Number 6021 by sanusihammed last updated on 10/Jun/16

$2^{x} + 2 x = 8$ $f i n d t h e v a l u e o f x$
Commented by Yozzii last updated on 10/Jun/16

$x = 2$ $2^{2} + 2 \times 2 = 4 + 4 = 8$
Commented by sanusihammed last updated on 10/Jun/16

$i t h i n k t h a t i s t r i a l a n d e r r o r$
Commented by Yozzii last updated on 10/Jun/16

$Y e s i t i s .$
	Answered by prakash jain last updated on 10/Jun/16

	$x = u + 4$ $2^{u + 4} + 2 (u + 4) = 8$ $2^{u + 4} + 2 u + 8 = 8$ $8 \cdot 2^{u} + u = 0$ $8 \cdot 2^{u} = - u$ $8 = - \frac{u}{2^{u}} = - \frac{u}{e^{u \ln 2}}$ $8 = - {u e}^{- u \ln 2}$ $8 \ln 2 = - u \cdot \ln 2 \cdot e^{- u \ln 2}$ $W (8 \ln 2) = - u \ln 2$ $- u = \frac{W (8 \ln 2)}{\ln 2}$ $(4 - x) = \frac{W (8 \ln 2)}{\ln 2}$ $x = 4 - \frac{W (8 \ln 2)}{\ln 2}$ $W is \log product function .$
	Commented by Rasheed Soomro last updated on 10/Jun/16

	$C a n w e c a l c u l a t e f u r t h e r$ $x = 4 - \frac{W (8 \ln 2)}{\ln 2} = 2$ $B e c a u s e 2 i s o b v i o u s r o o t o f t h e g i v e n$ $e q u a t i o n .$
	Commented by sanusihammed last updated on 10/Jun/16

	$I n t d r d s t i n g .$ $p l e a s e i d o n t k n o w w h a t i s p r o d u c t l o g . . . . .$ $s o r r y f o r a s k i n g t o o m u c h q u e s t i o n .$ $i w i l l l o v e t o k n o w h o w t h e p r o d u c t l o g i s e x p r e s s$
	Commented by FilupSmith last updated on 10/Jun/16

	$Wikipedia has a lot of information$ $on the product \log . So does wolfram alpha$ $a good old google search is your best$ $friend! :)$
	Commented by prakash jain last updated on 10/Jun/16

	${Rasheed}^{'} s comment$ $W (8 \ln 2) = 2 \ln 2 (Wolfram alpha)$ $so x = 2$
	Commented by Rasheed Soomro last updated on 11/Jun/16

	$THANKS!$
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