Originally Posted by

**billco**
All three of my Scientific calculators clearly distinguish 'ln' from 'log'

"In our calculator we trust" -every engineer I've met

In the vast majority of mathematics, texts, journal articles, lectures, etc. "log" will denote the logarithm to base "e". This is the most common and usefull log that comes up for mathematicians, so it has a good hold on this notation in maths. "ln" doesn't generally appear. The main exception is your calc texts aimed at science and engineering students, which will agree with your trusted calculators (which weren't made with mathematicians in mind).

A capital "L" on the "Log" is rare, most common in my experience in complex analysis texts to denote a specific branch of the logarithm they commonly use throughout the text. They'll use "log" if they want to leave it unspecified.

Notation isn't standard, get used to it. I've seen many lectures/articles where a subscript on the log denotes iterations (of course they explicitely explained this) i.e. log_3(x)=log(log(log(x))), because it was convenient to have a notation for such a thing, and the only base of log that will be encountered was 'e', (or the base just didn't matter, this is often enough the case).

The moral, if you see "log" in a strange location and the base does matter, take a moment to figure out the context and if this determines the base. In the OP, it should be clear given this recognizable series (c'mon, you've all seen the series for log(1-x), even the engineers). If the base doesn't matter, just pretend it's your favorite if it makes you more comfortable.