Is there a closed form?

Calculus Level 5

It is given that there is a value xx such that

xy=yx  (x>1){x}^{y} = {y}^{x}\ \ (x>1)

has only 11 solution for yy. Let that solution for yy be AA.

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

Details and Assumptions

  • If you think that there is more than 11 such value for yy, input -1.

  • If you think that there is no such value for xx, input 2.

  • xx and yy are real.


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