Examples? Which examples? Do you mean the snippets of documentation I am attaching at the end? Sure, they do!
The problem is the actual math/physics formalism is not!
The problem is the actual math/physics formalism is not!
Sure physics (and sometimes mathematics) do use the notation 'ln' every so often (if only because it's shorter) but you'd be hard pressed to find a reference in anything related to mathematics or physics that uses log as the base 10 logarithm.
Clearly the easiest way to avoid the ambiguity is to only ever use the natural logarithm, which is the choice made by all the programming languages you listed at the end. And since you don't list any references where log should refer to the base-10 logarithm I'll have to conclude that they made the right choice.