Is there a closed form?

Calculus Level 5

It is given that there is a value \(x\) such that

\[{x}^{y} = {y}^{x}\ \ (x>1)\]

has only \(1\) solution for \(y\). Let that solution for \(y\) be \(A\).

Find \(\left\lfloor 10000A \right\rfloor. \)

Details and Assumptions

  • If you think that there is more than \(1\) such value for \(y\), input -1.

  • If you think that there is no such value for \(x\), input 2.

  • \(x\) and \(y\) are real.

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