Algebraic and transcendental solutions of some exponential equations
Abstract
We study algebraic and transcendental powers of positive real numbers, including solutions of each of the equations xx=y, xy=yx, xx=yy, xy=y, and xxy=y. Applications to values of the iterated exponential functions are given. The main tools used are classical theorems of Hermite-Lindemann and Gelfond-Schneider, together with solutions of exponential Diophantine equations.
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