# Repeating Power

Calculus Level 4

$\Large{ e^{x+e^{x+e^{x+e^{x+\cdot^{\cdot^\cdot}}}}}=10}$

Find the value of $$x$$ satisfying the infinitely nested function above.

Enter 0.666 if you come to the conclusion that no such $$x$$ exists.
Clarification: $$e$$ denotes Euler's number, $$e \approx 2.71828$$.