Question Number 7869 by FilupSmith last updated on 22/Sep/16
$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{numerical}\:\mathrm{value} \\ $$$$\mathrm{for}\:{x}\:\mathrm{in}: \\ $$$${xe}^{{x}} =\mathrm{1} \\ $$
Commented by FilupSmith last updated on 22/Sep/16
$${x}={W}\left({xe}^{{x}} \right) \\ $$$$\therefore\:{x}={W}\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{But}\:\mathrm{what}\:\mathrm{is}\:{W}\left(\mathrm{1}\right)=??? \\ $$
Commented by sou1618 last updated on 22/Sep/16
![I find it on Wiki. W(1)=ω=0.56714329... (omega constant) ω is defined by [ωe^ω =1]](Q7871.png)
$${I}\:{find}\:{it}\:{on}\:{Wiki}. \\ $$$${W}\left(\mathrm{1}\right)=\omega=\mathrm{0}.\mathrm{56714329}...\:\left({omega}\:{constant}\right) \\ $$$$ \\ $$$$\omega\:{is}\:{defined}\:{by}\: \\ $$$$\left[\omega{e}^{\omega} =\mathrm{1}\right] \\ $$