Change of base formula for Tetration

[jaydfox]

Regardless, if the proof has already been shown, then combined with my change of base formula, we now have a unique solution to tetration of bases greater than eta.

As it appears to me your change of base formula works merely for base \( b \) greater than \( \eta \) and \( a<b \).

How do you figure that it only works for a<b? It works for any two bases greater than eta, regardless of relative size. Actually, it works for any two bases greater than 1, though for bases less than or equal to eta, it only serves to find the change of base for the continuously iterated logarithms of infinity, relative to each other, which isn't quite the same thing as tetration (defined as continuous exponentiation from 0 or 1 or b, which can't get above the asymptote).