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Question Number 7869 by FilupSmith last updated on 22/Sep/16

$$\mathrm{How}\mathrm{do}\mathrm{you}\mathrm{find}\mathrm{the}\mathrm{numerical}\mathrm{value}$$$$\mathrm{for}x\mathrm{in}:$$$${xe}^x=1$$

Commented by FilupSmith last updated on 22/Sep/16

$$x=W\left({xe}^x\right)$$$$\therefore x=W\left(1\right)$$$$$$$$\mathrm{But}\mathrm{what}\mathrm{is}W\left(1\right)=???$$

Commented by sou1618 last updated on 22/Sep/16

$$IfinditonWiki.$$$$W\left(1\right)=\omega =0.56714329...\left(omegaconstant\right)$$$$$$$$\omega isdefinedby$$$$[\omega e^{\omega }=1]$$

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