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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 Wfunction 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 Wfunction. (1) $\displaystyle \: W_{0} \left(\frac{\ln x}{x}\right)=\ln x$ for $x<e$. (2) $\displaystyle \: p^x =ax +b $ has solution $\displaystyle (\ln p)^{1} W\left(a^{1} \ln p \cdot p^{b/a}\right)\frac{b}{a}$. Last edited by skipjack; August 13th, 2019 at 08:15 AM. 
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 $\displaystyle t = 10  W\!\left(\frac{e^{10}}{10}\right)\!$. 

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