Abstract
We denote the real logarithm of a positive number a by ln a, so that ax = exp (x ln a), and we shall discuss what is known about the real solutions x of the equation
(1)
$$x = {a^x},\;\,a > 0.$$
First, as exp t > 0 for all real t, each real solution x of (1) is positive.
Publisher
Cambridge University Press (CUP)
Reference10 articles.
1. On an application of Lambert’s W function to infinite exponentials;Galidakis;Complex Variables,2004
2. 4. Euler, L. , De formulis exponentialibus replicatis, Opera Omnia, Series Prima XV (1927) pp. 268-297
3. Acta Acad. Petropolitanae 1 (1777) 38-60.
4. A Note on Complex Iteration
5. The convexity of the function y = E(x) defined by xy = yx