I want to find the inverse of the function $y=x^x$ in implicit form and not by using Lambert W function. Can you tell me how to find it?
Thanks.
2026-02-23 10:03:23.1771841003
Inverse of the $y=x^x$ in implicit form?
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The Lambert $W$ function was precisely introduced to solve the equation
$$y=xe^x$$ and those that can reduce to that form, such as
$$\log y=\log x\,e^{\log x}.$$
That essentially means that there is no other way.