Inspired by Otto Bretscher

Algebra Level 4

$\huge x^{x^{.^{.^{x^{\pi}}}}}=\pi$

Find all positive solutions $x$ of the equation above.

Notation: $\pi=3.14159...$

This question is part of the set All-Zebra

None of the given options.

\sqrt{\pi}

No solution exists

\sqrt[\infty]{\pi}

\sqrt[\pi]{\pi}