tetration base conversion, and sexp/slog limit equations

[bo198214]

In your equations, what does \( {\exp_b}^{\circ n}(x) \) mean? And what does \( {\log_b}^{\circ n}(x) \) mean? I assume this is the mathematical shorthand for iterating "n" times.

Yes, but its not that common in higher mathematics. I use it to distinguish from the multiplicative power \( f^n(x)=f(x)^n \).

What does \( \text{slog}_{\eta}(x) \) mean? Is it restricted to values of x<e? And doesn't that limit the usefulness of the equation?

Yes you are right, lets forget about that idea.