

The most interesting logs in the world - weinzierl
http://www.johndcook.com/blog/2012/11/15/logarithms/

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CoolGuySteve
Pretty basic notation problem that was solved in my undergrad math program by
writing ln (pronounced "lawn") instead of log to denote natural log.

All the math I do now uses lg, so I didn't realize the ln convention isn't
common.

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pflats
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"

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Evbn
Ln-lin is the same as log-lin, since the only difference is a scaling
constant, which is fixed by adjusting the position of the lines by the same
scaling factor.

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johndcook
Please see this follow-up post: Approximation relating lg, ln, and log10

[http://www.johndcook.com/blog/2012/11/24/approximation-
relat...](http://www.johndcook.com/blog/2012/11/24/approximation-relating-lg-
ln-and-log/)

~~~
Evbn
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.

