This thought came to me when I was thinking about exponents. Is the only solution for $x^y=y^z$ be $x=y$? How exactly would we prove there are no other numbers or how would we exactly solve this?
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5Well, $2^4=4^2,$ so they don't have to be equal. – Cameron Buie Sep 16 '19 at 01:04
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All you can assume is $\frac{\ln y}y=\frac{\ln x}x$, obviously assuming $x,y\neq 0$ – Rushabh Mehta Sep 16 '19 at 01:06
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@3above Oh that’s true. Then what about $x^y=y^z=z^x$? Or in fact up to an infinite amount variables? – Physics_Learner Sep 16 '19 at 01:15