Please-show-me-an-approach-to-solve-this-2-x-4x-Find-the-value-of-x-

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 \dots

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 .