Please show me an approach to solve this... 2^x = 4x Find the value of x


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Question Number 5734 by sanusihammed last updated on 25/May/16

$P l e a s e s h o w m e a n a p p r o a c h t o s o l v e t h i s . . .$ $2^{x} = 4 x$ $F i n d t h e v a l u e o f x$
	Answered by prakash jain last updated on 25/May/16

	$2^{x} = 4 x$ $1 = \frac{4 x}{2^{x}}$ $1 = \frac{4 x}{e^{x \ln 2}} = 4 {x e}^{- x \ln 2}$ $\frac{1}{4} = {x e}^{- x \ln 2}$ $\frac{- \ln 2}{4} = - x \ln 2 e^{- x \ln 2}$ $W (- \frac{\ln 2}{4}) = - x \ln 2$ $x = - \frac{W (- \frac{\ln 2}{4})}{\ln 2}$ $W is product logarithm function$ $W ({x e}^{x}) = x$ $S o W (- x \ln 2 e^{- x \ln 2}) = - x \ln 2$
	Commented by Yozzii last updated on 26/May/16

	Commented by Yozzii last updated on 26/May/16

	$I n c a s e y o u w a n t e d a b i t m o r e$ $i n f o r m a t i o n o n W .$
	Commented by Rasheed Soomro last updated on 26/May/16

	$H o w y o u d e r i v e d \frac{- \ln 2}{4} = - x \ln 2 e^{- x \ln 2}$ $f r o m \frac{1}{4} = {x e}^{- x \ln 2} ?$ $P l e a s e i n s e r t s o m e s t e p s m o r e .$
	Commented by prakash jain last updated on 26/May/16

	$Multiplied both sides by - \ln 2$
	Commented by Rasheed Soomro last updated on 26/May/16

	$T h a n k S! I c o n s i d e r e d - x \ln 2 e^{- x \ln 2}$ $a s - x \ln (2 e^{- x \ln 2}) . S o {c o u l d n}^{'} t u n d e r s t a n d .$
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