2-x-2x-8-find-the-value-of-x-

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 \dots . .

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!