Comparing the Known Tetration Solutions

[jaydfox]

If by my solution you mean through parabolic iteration of

No, I meant the piecewise infinite differentiable definition of slog.
Isnt it defined for arbirtrary bases? (I think you wrote for base greater 1.)

No, the slog function is only defined for bases greater than 1. For bases between 0 and 1, the tetration function is not one-to-one, so its inverse is not a function, because there are multiple values. It's much like saying that y=x^2 does not have an inverse function. y=sqrt(x) only covers part of the domain of the original function.

Also, there's a question about whether you consider the slog function to only apply to the inverse of the function of iterated exponentials/logarithms from 1. For b=2, for example, the domain of slog is negative infinity to 2. However, you can perform iterated exponentials/logarithms from any real number as a starting point, so you could also include the graph for x>4 and the corridor between 2 and 4.