As nouns the difference between tetration and superlogarithm

is that tetration is (arithmetic) the arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ^b''''a'' denoting ''a'' to the power of ''a'' to the power of to the power of ''a'', in which ''a'' appears ''b'' times notation: ^''b''''a'', ''$a\backslash uparrow\backslash uparrow\; b$ ''or $a\backslash rightarrow\; b\backslash rightarrow\; 2$ while superlogarithm is (mathematics) one of the two inverse functions of tetration.