\(x^x=y^y\) part 2

Algebra Level 4

The graph of \(x^x =y^y\) where \(x\) and \(y \) are in the interval \((0,1)\) consists of a curve and a straight line (which is \(y=x\)), as shown. Let the intersection point be \((p,p)\). Find the value of \(\lfloor 100000p \rfloor\).

\(\)
Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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