No. Usually log without further specification is base10.
Except in mathematics and physics, where it usually is base e.
Except sometimes in computer science, where it can be base 2.
But there are more of those weirdnesses: "ld" can be "log decimal", so base 10; or "logarithmus dualis", so base 2. Base 2 is also sometimes written as "lb" (log binary). You really need to know the conventions of the field/subfield to know which is which.
Base 2 is also sometimes abbreviated lg.
Log without a basis (at least to me) usually indicates that the basis doesn't matter in this context (or is obvious).
I usually see either base e or base 2 as the default. In which applications do people use both logarithms and base 10 as the default? I mean, especially these day. In the olden days of the slide ruler base 10 was probably more common.