And then we say that it's not possible

Algebra Level 3

$x$ is a non-negative real number which satisfies the following equation.

$\huge x^{x^{x^{x^{.^{.^{x^{16}}}}}}}=16$

Then find the value of $x$ . Correct your answers to three decimal places.

Enter 666 if you come to the conclusion that no such $x$ exists.

This question is part of the set All-Zebra