That's stupid. Log should always mean natural log. Other bases are only used for edge cases, and of course they're simply a multiple anyway.
I'm pretty sure that popular convention says that log(x) is base 10 unless otherwise specified. That's what I learned, that's what my calculators did, and that's what Google does with their online calculator.
Depends on the field.
I've seen several people say this on this forum and I would love to know in what field(s) this is correct. Is it a mathematician thing, perhaps? Between degrees in chemistry, chemical engineering, and neuroscience, including two years of physics and two years of calculus, plus a decade and a half of various reading, I have never encountered this.
Mathematician here. When teaching calculus, log to me means base 10, and ln means base e. Beyond that level, I almost never say "natural log", I just say "log" and hope the listener assumes it's base e. I still might write ln though (with a cursive l, so it won't look like a 1).
In any case, mostly the constant multiple difference doesn't matter anyway in my experience. I imagine that would be different as soon as you try to apply it to the "real" world.