Is max entropy invariant under choice of base? Suppose I have a set of probability mass functions $S_1,\dots,S_n$ and I find that $S_j$ has the greatest entropy using the traditional formula for entropy using $\sum_{i\in S}-p_i \log_2(p_i)$.
In this case we're using a base of 2. Is it guaranteed that if instead I used any other base greater than 1 that I would find that $S_j$ has the greatest entropy?
Seems like this would be a needed property in information theory, otherwise it seems like it would be hard to argue we're interested in dividing the space into halves instead of thirds or fifths etc...

Expanding my comment into an answer:
The maxima are the same, because entropy in one base is a constant multiple of the entropy in another. It's a unit conversion—for example, base $2$ measures entropy in bits, and base $e$ measures entropy in nats.
As OP notes, this is because $\log_b(x) = \log(x) / \log(b)$.
