An exponential automorphism of the complex numbers $\Bbb C$ is a function $a: {\Bbb C} \rightarrow {\Bbb C}$ such that $a(z + w) = a(z) + a(w)$ and $a( e^z) = e^{ a(z)}$ for all $z, w \in \Bbb C$ Jan Mycielski (Problem 12301, Amer. Math. Monthly 129 (2022), 186) asked if $a(\log 2) = \log 2$ and if $a(2^{1/k}) = 2^{1/k}$ for $k = 2, 3, 4$. We solve these problems.
Mel Nathanson