My Math Forum how can I solve x/ln(x)=n

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 August 13th, 2019, 04:42 AM #1 Newbie   Joined: Aug 2019 From: israel Posts: 1 Thanks: 0 how can I solve x/ln(x)=n Hi, I am working on some program and the answer for this education is very important. Should I use Lambert W-function and if I do then how? Can any one send the steps for solving this problem, for example? x/ln(x)=100 Okay, the answer to this can help me as well: 10t+e^t=100 Last edited by skipjack; August 13th, 2019 at 09:09 AM.
 August 13th, 2019, 06:30 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 708 Thanks: 96 Apply Lambert W-function. (1) $\displaystyle \: W_{0} \left(-\frac{\ln x}{x}\right)=-\ln x$ for $x  August 13th, 2019, 09:05 AM #3 Global Moderator Joined: Dec 2006 Posts: 21,015 Thanks: 2250 For the first problem,$x = e^{-W_0(-1/100)}$or$e^{-W_{-1}(-1/100)}$. For the second problem, the real solution is$\displaystyle t = 10 - W\!\left(\frac{e^{10}}{10}\right)\!\$. Thanks from topsquark

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