Question

Solve for x>0, e^x^e^x^e^x^... = 2

Answer 1

\[e^{x^{e^{x}}} \] till infinity =2 = y (say)


\[=e^{x^{y}}\]

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

Therefore,
\[x^2 = \ln2\]
x = ln2

Greetings!

Answer 2

Oh wow, thanks, I didn't think about that approach!

Answer 3

welcome :-)

Answer 4

Sorry, I know its obvious but its \[\sqrt{\ln2}\]