Why Log and not Ln ?

The common mathematical notation for the natural log is log. One writes log10 for the base 10 log or log2 for the base 2 log. Of course, you are free to use ln, but there are reasons to grow up and make the switch:
Why is log used in serious programming languages? Because earlier in computer science, writers of programming languages were also fluent in mathematics (there was a time when math and comp sci were close together). The language designers knew what they were doing and were not obsessed with the 10 fingers on their hands. There is of course also some historical reason. Fortran for example used LOG and many programming languages followed.

Programming languages

Higher math

Here are a few screen shots of books with a bit more advanced math than calculus. Examples of books where ln is used are basic calculus books Stewart.

Ahlfors

Apostol

Conway

Landau

Lang

Loomis Sternberg

Rudin

Edwards

Stopple

Feynman