# 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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