"log" is "whatever base makes most sense in context". In a pure mathematics context, sure, "log" is base e, but in some places it's base ten, in computer contexts it's almost always base 2 and elsewhere it could be anything.

"ln" is unambiguous in all contexts. logarithmus naturalis is always base e. And so, since I'm a cross-discipline amateur, I'll use "ln" every time.

Consider WolframAlpha that likes to give results in terms of "log", meaning base e. If you feed its output back into it, it will give the option to change which base your log is supposed to be because it can't be sure. It's like it can't read its own handwriting. Use "ln" and it won't do that.