Super-logarithms are inverse functions of tetrational functions. Super-logarithms are variously written using the following notations

but on this page, we use the mnemonic notation *slog* exclusively.

Super-logarithm functions were originally defined over a sparse domain, which consisted of {0, 1, `a`, `a`^{a}, ...} and so on, because these are the only points defined for integer tetration.
In order to extend this definition to real numbers or complex numbers,
advanced mathematics is required to find a function that satisfies both
infinite differentiability and the definition of super-logarithms:

where and .