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Symmetrical equation

Question

How many solutions exist for xy = yx? xy=yx

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Should we assume that x and y are always unique values?

If x=y, then there are an infinite number of solutions.

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Count your example as one of the "solutions."

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how bout...

y = log(x)

x^log(x) = log(x)^x

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...or more in general...

Let y=f(x)

Solve f(x)x=xf(x) for x. There are unlimited number of y=f(x) for which a real solution exists for f(x)x=xf(x)

For example, let y=2x. Solving (2x)x=x2x results in x=2. Therefore, y=2x=4. 2^4=4^2.

Another example is what CaptainEd found above

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As long as y > 0 there always exist a solution.

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