So there are several ways of finding general positive solutions for the equation $x^y=y^x$. But does this equation appear anywhere in physics or other science ? Or maybe there is some practical purpose for it. Thanks in advance.
2026-03-25 11:02:23.1774436543
Applications of equation $x^y=y^x$
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The solution is essentially given by the Lambert W function, for which you can find a list of applications on Wikipedia:
https://en.wikipedia.org/wiki/Lambert_W_function#Applications
Does this help?