Logarithm in x^y = y^x?

Question

Since log (a^b) = b log a, shouldn't I be able to take the log of both sides of x^y = y^x, and get: x log y = y log x --> x = (y log x)/log y?

I have plugged in values however, and it doesn't work. Why is that?

Answer 1

Yes, it should. What numbers did you plug in? Most pairs of numbers will not work.

Lets reorganize the equation in a different way.

as you said x log y = y log x

now divide by x * y

(log x)/x = (log y) / y

its pretty clear that this cannot be true except when x = y

So your use of algebra was accurate, but it is a generally untrue formula.