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High Quality Content by WIKIPEDIA articles! 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. The precise definition of the super-logarithm depends on a precise definition of non-integral tetration (that is, yx 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 range.