(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine all positive rational solutions of x^y=y^x.

2. Relevant equations

3. The attempt at a solution

Obviously, x=y will always work. I think that is the only solution. If I can show that x^y must be rational, I think it will be easy because then both x and y must have the same primes in the numerator and the denominator. I tried writing out x=r/s, y = t/u, and manipulating, which leads to

[tex]r^{ts} u^{ru} = s^{ts} t^{ru} [/tex]

which is really not helpful.

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# Homework Help: Larson 3.3.25

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