It depends on the field.

For example in programming base e is more common. For example log is base e in C/C++, JavaScript, Java, Python, Perl, Mathematica, Fortran, and Rust.

Another example is number theory. I just checked a few number theory books from my library and most used base e: Hardy & Wright's "An Introduction to the Theory of Numbers", Apostol's "Introduction to Analytic Number Theory", Baker's "A Comprehensive Course in Number Theory", Ingham's "The Distribution of Prime Numbers", Baker's "Transcendental Number Theory", Ribenboim's "The Book of Prime Number Records", Kumanduri & Romero's "Number Theory with Computer Applications", and Niven's "Irrational Numbers".

The only number theory book I found using ln rather than log was Gelfond's "Transcendental & Algebraic Numbers".

If only! The math libs I know use the name `log` for base e logarithm, not `ln`.