Inspired by Abhay Tiwari

Calculus Level 4

\[\huge x^{x^{\cdot^{\cdot^{x^{e}}}}}=2\]

Find all positive solutions \(x\) of the equation above.

Clarification: The LHS represents an infinite power tower.

There is more than one solution None of the others \[x=2\] \[x=e^{1/e}\] There is no solution \[x=e\] \[x=\sqrt{2}\]

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