x-3-3-x-how-do-i-pls-use-lambert-to-find-x-3-

Question Number 151403 by 7770 last updated on 20/Aug/21

x^{3} = 3^{x}

h o w d o i p l s u s e l a m b e r t t o

f i n d x = 3

Commented by mr W last updated on 20/Aug/21

x = 3^{\frac{x}{3}}

x = e^{\frac{x}{3} \ln 3}

{x e}^{- \frac{x}{3} \ln 3} = 1

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

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

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

= {\begin{cases} - \frac{3}{\ln 3} \times (- 1.098612289) = 3 \\ - \frac{3}{\ln 3} \times (- 0.907473042) = 2.478053 \end{cases}

Commented by 7770 last updated on 20/Aug/21

t h a n k y o u s i r b u t h o w d i d u g e t (- 1.098612289) p l e a s e

Commented by mr W last updated on 21/Aug/21

u s e a n y m e t h o d f o r s o l v i n g e q u a t i o n s

n u m e r i c a l l y . t h e e q u a t i o n i s

{x e}^{x} = a

Commented by 7770 last updated on 21/Aug/21

o k s i r

t h a n k s

Commented by otchereabdullai@gmail.com last updated on 22/Aug/21

thank u