Super-logarithm
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms: * As the Abel function of exponential functions, * As the inverse function of tetration with respect to the height, * As a generalization of Robert Munafo's large number class system, For positive integer values, the super-logarithm with base-e is equivalent to the number of times a logarithm must be iterated to get to 1 (the Iterated logarithm). However, this is not true for negative values and so cannot be considered a full definition.The precise definition of the super-logarithm depends on a precise definition of non-integral tetration (that is, for y not an integer). There is no clear consensus on the definition of non-integral tetration and so there is likewise no clear consensus on the super-logarithm for non-integer inputs. (Wikipedia).
