The most interesting logs in the world

It's common everywhere except in ivory towers. Mathematical journals (english ones, at least) and the like use log to mean the natural log, because there's no need to use log_10 in any advanced/abstract system. (This is because 10 stops being a number of any import past being able to do arithmetic in your head; 10 is only special because we have that many fingers.)

The sciences have a definite use for log_10, since the metric system is based around powers of 10. A mathematician might argue that e.g. a log-lin graph would be just as useful with log_e as log_10, but then you lose the nice demarcations. It all depends who you're talking to and how they're using it.

As a professional mathematician, the author sees little need for log to mean anything other than the natural log. As a professional educator, I disagree. Clearly his readers are confused by the ambiguity of "log". He has a few options: do nothing and accept that inexperienced but curious mathematicians will be confused, use "ln" in place of "log" when writing wider interest instead of journal articles, or write a blog post complaining about it and hope the world will change to suit him.

edit: Although we pronounced ln "len" or "lin" instead of "lawn"

In grade school i was taught that ln is always base e, and lg is always base 10. log has to always come with a subscript, otherwise it's meaningless on it's own. In "real life" though, everyone seems to be using log and knows what it means, e.g. base 2 if it's information theory, base 10 if it's signal processing, base e if it's analysis, discrete logarithm if it's number theory, etc.

Same for me, also lb for base 2 logarithm.

Nice! Useless but fun example: ln 125 is approximately lg 125 - log 125 ~= lg 128 - log 100 = 7 - 2 = 5. Exact answer is close to 4.83, less than 5% error without ever thinking about a fractional value root or log.