How-do-you-find-the-numerical-value-for-x-in-xe-x-1-

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

$${I}\:{find}\:{it}\:{on}\:{Wiki}. \\ $$$${W}\left(\mathrm{1}\right)=\omega=\mathrm{0}.\mathrm{56714329}…\:\left({omega}\:{constant}\right) \\ $$$$ \\ $$$$\omega\:{is}\:{defined}\:{by}\: \\ $$$$\left[\omega{e}^{\omega} =\mathrm{1}\right] \\ $$

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