For Your Weekend Enjoyment

I generally use log for base e (sometimes writing ln though). If I need base 10, it's often because I'm working with RF, and it's all dB there anyway.

You missed out base 2 though, for all the information theorists.

I'm in psychology. When we use logs, the base is usually a parameter of a fit...

For me:

log = base 10
ln = base e

Often, log 2. Computer Science :)

Since ambiguous notation is one of my pet peeves, I stick to "log" for base 10, "ln" for base e, and specify the base for anything else. That said, I almost never actually use base 10. e is so much more... Natural.

Atomic physics.

-Mary

I choose to work in units where log_{10) e is unity, thus my work is notation-invariant. ;)

I tend to mean it in either the "It's better than bad, it's good!" sense or in the "Captain's" sense.

I may not be your target audience...

log == base 10
ln == base e

Physics

When writing it down, 'log' means base 10, and 'ln' means base e. But when speaking, 'log' usually means base e, because 'natural log' is too long. Added verbal clarification is rarely needed.

Field: aerospace, but only the space side

It depends.

Most computer languages have 'log' as Naperian, and so in writing algorithms, Naperian is the default, requiring a special function for Briggsian logarithms, something like "log10(x)".

At the same time, decibels (and bels) are so deeply rooted in engineering that Briggs trumps Napier.

So it depends on the 'hat': with the math hat on, Napier; with the engineering hat, Briggs.

I used log for base 10, ln for e while doing chemical engineering work.

I don't use log for anything in software development. It's funny that comp sci and math are considered so strongly linked but a good chunk (possibly most) of commercial software development uses nothing more complicated that basic algebra.

I write ln to refer to the natural log, and when I read "log", I assume it is in base e.

I can't remember the last time I used log_10, if I ever had to write log_10 I would probably add the subscript to remove ambiguity

I am in physics (officially a grad student in a week or so)

I'm with the majority it looks like...

log is base 10, unless i'm talking computers, in which case it's sometimes base 2, though i try to be explicit about any base that isn't 10.

base e is always (not that i use it much these days) ln.

p.s. @skwid : lol, thanks for brightening my day...

Log(x) ==> base 10
Ln(x) ==> base e
Lg(x) ==> base 2

Anything else, specify. Log and Ln are pronounced differently, too.

Sheesh. This is something where there actually is a correct answer across the various disciplines. (Mine being engineering and CS.)

log ("log") is base 10, ln ("lawn") is base e

chemistry/engineering-environmental

I thought ln x (yes, base e) was pronounced "lun" or maybe "lin" or "len", not "lawn." But the distinctions I see here about written convention are correct.

"Profession": moderate polymath, interdisciplinary gadfly.

Originally:
"log" := (any) log function
"Log" := P.V. for (any) log function
"lg" := log10
"Lg" := PV(log10)
"ln" := loge
"Ln" := PV(loge).

But in english "log" for log10 and loge for loge . :-P

Seems I can revert to "ln" and "Ln" though.

Base e of course. I'm a physicist.

Base 2

In bioinformatics, we analyze a lot of microarray data, where the probes have values based on a log2 ratio.

Base e, I'm thinking. I'm a math/theology student.

log = log10ln = logeChemistThough when speaking, I will say "log" for either, as long as the context makes it clear which is appropriate.

log10 == log10
log == loge

I do what math.h tells me!

This said, I do have to admit there have been times in the past that I couldn't remember offhand exactly what base plain "log" would give me in some programming environment or other, so just so that I wouldn't have to look it up I would just say something like log(x)/log(10). Hey, it'll always work, so might as well, right?

I have no default for "log". I would only ever write it without a subscript if it were base e and even then only if it were crystal clear from context that that was meant. Comes from knocking around too many disciplines with too many divergent conventions.

Assuming bare "log" is base 10 is actively dangerous IMO - far too many contexts assume it's base e.

For astronomers, log=log10. We love those Powers of Ten.

I prefer logarithms to the base pi.

See, for example:

http://www.research.att.com/~njas/sequences/A104288

A104288 Decimal expansion of log base pi of 2.
6, 0, 5, 5, 1, 1, 5, 6, 1, 3, 9, 8, 2, 8, 0, 1, 5, 7, 3, 4, 8, 8, 0, 0, 5, 4, 5, 2, 3, 9, 8, 4, 7, 2, 9, 8, 6, 2, 9, 9, 8, 0, 8, 8, 7, 6, 8, 8, 2, 8, 6, 3, 2, 4, 8, 6, 3, 9, 1, 6, 3, 8, 4, 5, 5, 7, 7, 5, 3, 6, 5, 5, 7, 9, 7, 8, 5, 5, 8, 5, 5, 6, 6, 2, 6, 1, 0, 9, 4, 1, 9, 2, 3, 2, 0, 7, 4, 6, 5, 3, 9, 8, 8, 9, 1

FORMULA

log(2) / log(pi)

EXAMPLE

0.605511561398280157348800545239847298629980887688286324863916384557753655797855855662610941923207465398891...

KEYWORD

cons,nonn

AUTHOR

Bryan Jacobs (bryanjj(AT)gmail.com), Feb 28 2005

I suppose, having authored the post, I should participate, too:

log is always base e.

log is base e, of course. Why on earth should Nature care how many toes our species happens to have?

Anything else is log x / log b, and then quickly absorb the log b into somewhere. And I'm in string theory.

My field is materials science and engineering. Since in the traditional fields of ceramics and metallurgy you still come across "experienced" professionals who still remember the days of sliderules, saying "log" always refers to base 10. To refer to base e, you say "natural log".

Heck, when you're dealing with corrosion experts and electrochemists, you deal with people who put the Nernst equation into the form

E = Eo + (2.3RT/nF) log(Co/Cr)

in order to explicitly work with log base 10.

And I know this has no real scientific standing, but Excel uses the LOG command for base 10 and LN for base E. So the answer is clear, at least for the general population.

Oh, and I guess I should toss in the complexity theorist perspective to all this:

The question is meaningless, as log10, loge, and log2 are all equal. There is no base. There is only "log".

log - base 10
ln - base e

Electrical engineer

log is base 10, ln is base e... chemical engineer

I usually think of it being base e, but that's likely due to the crowd of physicists and mathematicians I hung out in uni. Generally, we were taught that lg is base 10 and ln is base e (with everything else being specified, but that doesn't really seem to hold in North America).

log always refers to base e. In print, in speech, wherever, unless specified otherwise...which rarely happens. It's not really my choice, but this is the convention, and not following it can leave you confused at meetings.

I'm in physics.

I usually mean base 2, but I am one of them crazy information theorists. The fact is though, the base doesn't really matter, base 2 is just convenient.

I basically just want to win the 500k comment drawing, so I can't think of a lot to say about logs right now (except, it;s the music made by lumberjacks while rolling those cut stumps down the river...)

Related digression: So, what is 0^i? It is hard to figure out. I mean, 0^1 = 0 and 0^(-1) is undefined but limits to infinity, so ... ?

#35: don't forget:

i^(-i) = sqrt(e^pi)

For the sake of notational clarity, I always use log as base 10, ln is base e. Plus ln is a whole letter shorter! And so much simpler to write. I don't have to do the loop-dee-loop for the g, no o at all to deal with. "ln" is so much more efficient. =P

Of course, if I'm doing a contour integral or for some other reason working in the complex plane, then log is the complex valued logarithm, which is by default base e, and I use ln as the real part of the complex logarithm.

Spoken, log means base e, simply because I don't remember the last time I used base ten, and the only people with whom I tend to talk about logarithms are fellow physicists, so there's no chance of confusion. I used to be careful about writing ln instead of log for base e, and now I just do it out of habit. That may change as Mathematica tightens its grip on me in the coming years, though. I'm a high energy physics grad student.

base e. Usually I mean the formal power series: that works over any field of char. zero :-) My field is mathematics, of course.

Depends if I'm working with pencil and paper, or writing code.

With pencil and paper, ln(x) is base e. Anything else arises so infrequently that I specify the base.

The people who write computer languages don't see it that way. They use log() -- or worse yet, alog() (because Fortran thinks any function beginning with an L returns an integer, and IDL slavishly imitated Fortran) -- to mean base e. If you want base 10, there is log10() (or alog10()). Any other base b is log(x)/log(b). I sometimes use dB w.r.t. a specified reference level when analyzing electric or magnetic field spectra.

I'm in physics.

Jonathan V. Post, thanks but I don't see how to apply that to taking zero to a complex power...

Re #35,36,41:

"...A mathematical expression can also be said to be indeterminate if it is not definitively or precisely determined. Certain forms of limits are said to be indeterminate when merely knowing the limiting behavior of individual parts of the expression is not sufficient to actually determine the overall limit...."

"... There are seven indeterminate forms involving 0, 1, and infinity..."

"... If complex infinity is allowed as well, then six additional indeterminate forms result..."

http://mathworld.wolfram.com/Indeterminate.html

Aaron (and Chad),
I know these little polls seem like amusement, but I want to thank you for doing them. I really liked this particular poll because I had forgotten that people defined 'log' differently. And since I sometimes deal with physicists and mathematicians (not too many computer scientists though), it's good to remember that common words in our professional vocabularies don't have the exact same meaning.