Solve-for-x-3-2x-18x-

Question Number 14853 by tawa tawa last updated on 04/Jun/17

Solve for x

3^{2 x} = 18 x

Answered by mrW1 last updated on 04/Jun/17

e^{2 x \ln 3} = 18 x

18 {x e}^{- 2 x \ln 3} = 1

(- 2 x \ln 3) e^{(- 2 x \ln 3)} = - \frac{\ln 3}{9}

\Rightarrow - 2 x \ln 3 = W (- \frac{\ln 3}{9})

\Rightarrow x = - \frac{W (- \frac{\ln 3}{9})}{2 \ln 3} \approx - \frac{W (- 0.122068)}{2.197225}

= {\begin{cases} - \frac{- 3.295837}{2.197225} = 1.5 \\ - \frac{- 0.140479}{2.197225} = 0.063935 \end{cases}

Commented by adelson last updated on 05/Jun/17

{w h a t}^{'} s W ?

Commented by tawa tawa last updated on 05/Jun/17

God bless you sir .

Commented by mrW1 last updated on 05/Jun/17

W s t a n d s f o r L a m b e r t W - f u n c t i o n

w h i c h i s t h e i n v e r s e f u n c t i o n o f

f (x) = {x e}^{x}

Commented by tawa tawa last updated on 05/Jun/17

Have been wondering, please sir explain further .

Commented by mrW1 last updated on 05/Jun/17

I {d o n}^{'} t k n o w w h a t I c a n t e l l m o r e .

O n e s h o u l d k n o w t h a t f o r r e a l v a l u e s

W (x) f u n c t i o n i s d e f i n e d f o r x ⩾ - \frac{1}{e}

a n d f o r - \frac{1}{e} < x < 0 t h e r e a r e t w o v a l u e s

f o r W (x) .

Commented by tawa tawa last updated on 05/Jun/17

Alright sir . God bless you

Commented by tawa tawa last updated on 05/Jun/17

What i mean is that how do you get - 3.295837

Commented by mrW1 last updated on 06/Jun/17

i f y o u c a n n o t f i n d a W - f u n c t i o n

c a l c u l a t o r w h i c h g i v e s 2 v a l u e s f o r

x < 0, y o u c a n a l s o c a l c u l a t e b y y o u s e l f,

f o r e x a m p l e u s i n g g e o g e b r a . y o u

f i n d j u s t t h e z e r o p o i n t s f r o m f u n c t i o n

f (x) = {x e}^{x} + \frac{\ln 3}{9}

Commented by mrW1 last updated on 06/Jun/17

Commented by tawa tawa last updated on 06/Jun/17

God bless you sir .