Please verify my answer to this question about the domain

[abdv17]

Homework Statement

Find the natural domain of the function ln composed with itself n times.

Relevant Equations

ln(x) is defined only for x>0.

For n=1 (ln(ln(x))), the domain is the set of all real x>1 ;
for n=2, the domain is the set of all real x>e ;
for n=3, the domain is the set of all real x>e^e ;
for n=4, the domain is the set of all real x>e^(e^e)
...Thus, for a general n the domain is the set of all real x greater than e^(e^...^e^e) ,where there are n-2 terms in the parentheses.
(Sorry if this is confusing, I'm still trying to figure out LATEX.)

 

[fresh_42]

You should first figure out from where to where the logarithm goes: from to get the original domain, to because these are the domains of the iterations. Which values can you feed the logarithm with?

Then try to figure out what $\log^n(x)$ does.

And by the way, $\log^1(x)=\log(x)$.

Here is explained how you can type formulas on PF: https://www.physicsforums.com/help/latexhelp/

 

[anuttarasammyak]

Power tower https://mathworld.wolfram.com/PowerTower.html might be of your interest.