When you want the log, do you want the natural logrithm (written as ln in math but written as log in program) or the base 10 logarithm (written as log in math but written log10 in program)

I was about to assume you must mean natural log since it makes very little sense to take the base 10 logarithm of 10 raised to some power, but I realize that most people don't study math much and might not know that. And if it was written like that in some text it almost assuredly means log base 10.

ie. log(10^x) == x. log and 10^ are inverse operations. It's like having (5 * x) / x. They undo each other.