Let $X \in \text{Random} \{ x_1, \ldots, x_N \}$ be a D5723: Simple random variable.
Let $a, b \in (0, \infty) \setminus \{ 1 \}$ each be a D5407: Positive real number.

Then \begin{equation} H_b(X) = (\log_b a) H_a(X) \end{equation}