how can I solve x/ln(x)=n

Aug 2019
1
0
israel
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 a moderator:
Dec 2015
1,084
169
Earth
Apply Lambert W-function.
(1) \(\displaystyle \: W_{0} \left(-\frac{\ln x}{x}\right)=-\ln x\) for $x<e$.
(2) \(\displaystyle \: p^x =ax +b \) has solution \(\displaystyle -(\ln p)^{-1} W\left(-a^{-1} \ln p \cdot p^{-b/a}\right)-\frac{b}{a}\).
 
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skipjack

Forum Staff
Dec 2006
21,478
2,470
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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