f(x) = ln(ln(lnx)) has the domain of (e, infinity). I am not sure how this occurs however. I know in the case of ln x, x must be greater than 0. However where does e come from. e is the base of log in the case of ln, but something is just not clicking for me.

Answer 1

since ln(u) needs u>0,

ln(ln(ln(x))) needs ln(ln(x)) > 0
That is, ln(x) > 1
That is, x>e

Answer 2

I am still confused. hm.