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}