Let $x_1, \dots, x_N \in \mathbb{R}$ each be a D993: Real number.
A D993: Real number $a \in \mathbb{R}$ is an exponential mean of $x_1, \dots, x_N$ if and only if \begin{equation} \sum_{n = 1}^N e^a = \sum_{n = 1}^N e^{x_n} \end{equation}