hiw-do-i-solve-2-x-4x-

Question Number 76009 by Rio Michael last updated on 22/Dec/19

h i w d o i s o l v e

2^{x} = 4 x ?

Answered by mr W last updated on 22/Dec/19

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} = 0.3099 \\ - \frac{- 2.77258872}{\ln 2} = 4 \end{cases}

Commented by vishalbhardwaj last updated on 22/Dec/19

W = ? ? ? ? ? ? ?

Commented by mr W last updated on 22/Dec/19

L a m b e r t W f u n c t i o n :

W (x) \times e^{W (x)} = x

Commented by Rio Michael last updated on 24/Dec/19

s i r i w a n n a k n o w a b t t h i s w h y

a r e y o u t a k i n g e o n l y o n e o n e s i d e ?

Commented by Rio Michael last updated on 24/Dec/19

o k a y s i r a n d i n t h a t f o r m w e m a n u p u l a t e

a n d s o l v e f o r x .

Commented by mr W last updated on 24/Dec/19

t o u s e l a m b e r t W f u n c t i o n w e

s h o u l d a r r a n g e t h e e q u a t i o n i n t o

t h e f o r m (\dots) e^{(\dots)} = (\dots \dots)

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