What is the inverse of 1/logX?

Question

Also prove that 1/logx has an inverse!

Answer 1

(1) Simple inverse is log X as long as log is defined for the specific value of X, except that it's also not defined at X=1 since log(1) = 0.
(2) Inverse function: If Y = 1/logX, then X = exp(1/Y) assuming natural logarithms. This is defined except at Y=0, which can't hold for finite X.

The proofs of both these are trivial. They are obvious.