When you see log(x) do you think base e or 10.

[VTBoy]

I think base e, because in all of my college work it has been reffered to as base e.

[Nicolas]

In high school, we were very strict in that:

base e = natural logaritm, written ln(). I added to that "and NOT pronounced as LOG!"

base 10 = log()

other bases = 3log() 5log() (subscript)

base 10 may also be written 10log()

In University, it got all mixed up. Oh well, they can't even be clear on v for velocity vs V for volume here...

[clop]

Throughout 6 years of schooling, 5 years of university, and 13 years as an engineer

log(x) is log₁₀(x)

ln(x) is log_e(x)

I've never known anyone write log(x) and mean ln(x), nor the other way round.

clop

[Nicolas]

writing ln while meaning log is not something I've ever seen, but the other way around seems popular around here.

*extreme use of words kept for myself*

[jrkeller]

Throughout 6 years of schooling, 5 years of university, and 13 years as an engineer

log(x) is log₁₀(x)

ln(x) is log_e(x)

I've never known anyone write log(x) and mean ln(x), nor the other way round.

clop

I concur

[HenrikOlsen]

ditto

[VTBoy]

Perhaps it depends on your field. In mathematics and statistics log base 10 has almost no real use, but log base e is used extensivly.

[clop]

Isn't it fun that

log_e10 = log_x10/log_xe

Heh heh, I've never got over that.

clop

[Kristophe]

I've also never seen log(x) refer to the natural logarithm, not even in my math classes. In math classes, the professors always labled it log₁₀(x), but they always used ln(x) in the stead of log_e(x).

[Swift]

Throughout 6 years of schooling, 5 years of university, and 13 years as an engineer

log(x) is log₁₀(x)

ln(x) is log_e(x)

I've never known anyone write log(x) and mean ln(x), nor the other way round.

clop

Me too (American, chemist, ** and PhD). log would be pronounced "log" and ln as "lan"

[hhEb09'1]

Perhaps it depends on your field.

This wiki article says mathematicians (See comment by Halmos) use log for natural logs, and engineers use log for base 10. That's been my experience.

[Celestial Mechanic]

My usage has always been log for log₁₀ and ln for log_e. But I'm always prepared for whatever usage an author chooses, it can usually be determined from the context if the author doesn't specifically say so.

[Bignose]

FORTRAN uses LOG(X) for natural log and LOG10(x) for base-10 log.

[Nicolas]

Damned be Fortran!

Now on the pronounciation. How do you pronounce log? How do you pronounce ln?

I hear some people saying "log10" for log, and "log" for ln. VERY confusing IMO. I say "log" for log, and "ellen" for ln. There are girls in mathematics .

[VTBoy]

FORTRAN uses LOG(X) for natural log and LOG10(x) for base-10 log.

As does MatLab, Mathmatica, and Maple.

[Nicolas]

Luckily Ecosim does not. I don't know about Excel.

[FrostByte]

In my school(engineering) we use maple and if I'm not mistaken ln is in there. Correct me if I'm wrong, though. And they are quite strict in all theoretical lessons:

Log(x): base 10
Log y (x): base y with y as subscript
Ln(x): base e

I've never known it otherwise.

[peter eldergill]

We use ln(x) as a short form (but a bit backwards I suppose) as "natural logarithm", hence the "n" for natural...

In calculus (in high school), we have very little need for base 10 logs, except for making students memorize yet another derivative formula.

Occasionally we use it for earthquakes, decilbels, etc...but not much else.

I didn;t know the computer programs were different from what we teach. I suppose if you're using a math program which involves log10(x), you're probably bright enough to understand how the logs work and it wouldn't be much of a stumbling block

Pete

[Eta C]

From the start I was taught that absent an indicator "log(x)" was base 10 and "ln(x)" was base e. The fact that most calculators use this convention only strengthens the identification.

The origin of ln may be Latin. Short for "logarithmus naturalis" or some other properly declined Latin noun.

In my work I often deal with sound propagation through water. All of the source levels, propagation loss, etc, are expressed in decibels, so we make fairly frequent use of the log function.

[Argos]

When you say "log" I tend to think of it as base 10.

[VTBoy]

In my school(engineering) we use maple and if I'm not mistaken ln is in there. Correct me if I'm wrong, though. And they are quite strict in all theoretical lessons:

Log(x): base 10
Log y (x): base y with y as subscript
Ln(x): base e

I've never known it otherwise.

Woops you are right, I made a mistake. It is just MatLab and Mathmatica that refer to log as log base e.

[hhEb09'1]

Luckily Ecosim does not. I don't know about Excel.

I just checked my copy of Excel. Weirdly, it has LOG10 and LN functions, but the LOG function also defaults to base 10, although you can use any base by adding a second parameter, like LOG(8,2)=3

The origin of ln may be Latin. Short for "logarithmus naturalis" or some other properly declined Latin noun.

The wiki article I linked earlier says "The notation was in fact invented in 1893 by Irving Stringham, professor of mathematics at Berkeley"

[Celestial Mechanic]

Another oddity about the natural logarithm function: it is the only function whose iterated versions don't require parentheses, at least in written form. That is, everyone understands that

ln x
ln ln x
ln ln ln x

are

ln(x)
ln(ln(x))
ln(ln(ln(x)))

respectively. These forms are much more likely to occur than, say tan(tan(x)) or exp(exp(x)).

In programming languages and in spreadsheets the parentheses are required as with any other function.

[peter eldergill]

I would still write ln(lnx)) as my students might think that it's multiplication...sometimes they think that anyways....

Pete

[Eta C]

The wiki article I linked earlier says "The notation was in fact invented in 1893 by Irving Stringham, professor of mathematics at Berkeley"

Well, not to be out-wikied, the site for natural logarithm mentions that the French term is logorithme neperien after John Neper, a Scottish mathematician. So perhaps Stringham based it on the French.

[Nicolas]

Ah yes, Neper was his last name.

[Celestial Mechanic]

I would still write ln(lnx)) as my students might think that it's multiplication [Snip!]

Which is probably a good idea pedagogically. But note that you did not write parentheses around the x. That's OK, no one does that for elementary functions of a simple variable or constant, e.g., tan x, exp 1.5, arcsin 0.5.

But parentheses are always used with the more advanced engineering functions. You will never see the Bessel function J₂(x) written as J₂ x, for example.

[hhEb09'1]

Well, not to be out-wikied, the site for natural logarithm mentions that the French term is logorithme neperien after John Neper, a Scottish mathematician. So perhaps Stringham based it on the French.

If he (Napier/Neper/Marvellous Merchiston) was Scottish, why use the French?

After all, your wiki page says " Indeed, Nicholas Mercator first described them as log naturalis before calculus was even conceived"

[kashi]

Throughout 6 years of schooling, 5 years of university, and 13 years as an engineer

log(x) is log₁₀(x)

ln(x) is log_e(x)

I've never known anyone write log(x) and mean ln(x), nor the other way round.

clop

Clop says it like it is

[Nicolas]

Quick answer please,

When you see ln^2(x), does it mean

ln(ln(x))

or (ln(x))^2

(where "^2" means squared)