solve-2-x-2-8x-

Question Number 41390 by mondodotto@gmail.com last updated on 06/Aug/18

solve 2^{x - 2} = 8 x

Answered by MrW3 last updated on 06/Aug/18

\frac{2^{x}}{2^{2}} = 8 x

2^{x} = 32 x

e^{x \ln 2} = 32 x

32 x e^{- x \ln 2} = 1

(- x \ln 2) e^{- x \ln 2} = - \frac{\ln 2}{32}

\Rightarrow - x \ln 2 = W (- \frac{\ln 2}{32})

\Rightarrow x = - \frac{W (- \frac{\ln 2}{32})}{\ln 2} = {\begin{cases} - \frac{- 0.0221}{\ln 2} = 0.0319 \\ - \frac{- 5.5452}{\ln 2} = 8 \end{cases}

Commented by mondodotto@gmail.com last updated on 06/Aug/18

thank you sir, but what does W stand for

Commented by $@ty@m last updated on 06/Aug/18

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

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

t h e n x = W {f (x)}

i . e . W \equiv f^{- 1}

Commented by mondodotto@gmail.com last updated on 06/Aug/18

thanx