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curious guest
Jun-21-02, 00:11 AM (EST)

"how to solve x^x=a"

 I found the x^(x^3)=3 solution in the site quite interesting and was thinking: what about x^x=a? I have tried hard to solve the problem but i couldnt do it. And what of f(x)=a where f(x)=x^(x^(x^(x^x)))=a and there are n recurrent cases, similar to the one in the x^(x^3) page?

alexb Charter Member
749 posts
Jun-21-02, 00:19 AM (EST)    1. "RE: how to solve x^x=a"
In response to message #0

 >I have tried hard to >solve the problem but i couldnt do it. You probably tried to express the solution by means of the so-called elementary function, right? sin(x), cos(x), xn, ax, etc... This is impossible.The solution to xx = a is given by the Lambert function invent specifically for that purpose. See, for example,https://mathworld.wolfram.com/LambertsW-Function.html

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