While working out something in thermodynamics, I encountered an equation that had a term like $\log(n_1/n_2)$, where, $n_1$ and $n_2$ are the number densities. Now of course the argument of the $\log$ is dimensionless, but I can write the same as (at least mathematically) $\log(n_1)-\log(n_2)$, in which case we have inconsistency that the arguments are not dimensionless.
So even though, its mathematically possible, in the case of physics should we restrict from using this particular expression for $\log$ wherever we have some inconsistency?
EDIT : As it has been pointed out in comments, I am also interested in understanding in cases, where $n2$ or $n1$ is small since one can't use a series expansion !!