Lóczi, Lajos2024-09-042024-09-042003-12-01Teaching Mathematics and Computer Science, Vol. 1 No. 2 (2003) , 219-2331589-7389https://hdl.handle.net/2437/379506In this survey article we guide the reader through the solution of the commutative equation of exponentiation x^y = y^x and that of the associative equation of exponentiation x^(y^z) = (x^y)^z. Various characterizations of the integer, rational, real and complex solutions are discussed together with some new results and open directions. The article is supplemented by a detailed and commented bibliography on the history of these equations.application/pdfcommutativity of exponentiationassociativity of exponentiationparametrizations of the solution setfolyóiratcikkOpen AccessLajos Lóczihttps://doi.org/10.5485/TMCS.2003.0022Teaching Mathematics and Computer Science21Teach. Math. Comp. Sci.2676-8364