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

#### danielhaish

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

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#### idontknow

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
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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