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 loge(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 loge(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

loge10 = logx10/logxe

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 loge(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 loge(x)

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

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

[hhEb09'1]

Perhaps it depends on your field. This wiki article (http://en.wikipedia.org/wiki/Logarithm) 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 loge. 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)=3The 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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/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 (http://en.wikipedia.org/wiki/John_Napier)) 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 loge(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)

[Cuddles]

The second one.

I've always pronounced log as log and ln as loggy. I'm not sure if anyone ever understand me though.

[Nicolas]

And indeed they did mean the second one.

It took us another hour to find out whether sin-1 in a certain book meant arcsin (like on calculators) or 1/sin (like in many books). Nice....

[hhEb09'1]

And indeed they did mean the second one.

It took us another hour to find out whether sin-1 in a certain book meant arcsin (like on calculators) or 1/sin (like in many books). Nice....
I don't think I've ever seen ln^2(x) mean ln(ln(x)), or sin-1 mean 1/sin, do you have a book title and/or author?

[Tobin Dax]

I'd say log-squared, (ln(x))^2. The same thing applies to trig functions.

[Nicolas]

I don't think I've ever seen ln^2(x) mean ln(ln(x)), or sin-1 mean 1/sin, do you have a book title and/or author?

I can't recall ever seeing ln^2(x) meaning ln(ln()), but then again it was about the first time it was written that way in a formula that I needed. The meaning (ln(x))^2 is the most logical one, but I prefer to actually write it as (ln(x))^2 in order to avoid any confusion. In the same spirit, I also always write (sin(x))^2.

As for sin-1 meaning 1/sin, I don't know what literature writes it that way, but I learned that sin-1 only meant arcsin on calculators, and books tended to use asin or arcsin to avoid confusion with exponents. Apparently my chef also thought that way, as he assumed it was intended as 1/sin as well. I don't think it's something European, as many of the books used are US books.

If I remember well, my old math book used to state arcsin as arcsin, so sin-1 meant 1/sin. But I'm not sure, and I don't know where exactly our notion of sin-1 - 1/sin in books comes from, nor what books use it like that.

[hhEb09'1]

If I remember well, my old math book used to state arcsin as arcsin, so sin-1 meant 1/sin. Not necessarily. I just checked an old engineering calc book by Kreyszig and in it, both arcsin and sin-1 were used for the inverse of the sine function. I also checked a Calculus text by Salas and Hille, and it used arcsin, but it noted that "some American and British textbooks write sin-1" and it did not use sin-1 for 1/sin

[Nicolas]

With "my old math book" I literally meant mine, not as a general rule for any math book :).

Anyway, for me there is least confusion when log10 is log, loge is ln, ln squared is (ln(x))^2, the arcsin is asin or acrsin, and sin-1 is only used as 1/sin (preferably always write 1/sin anyway :)). But that's something for Utopia, as I constantly stumble on differences in t, T and T0, v and V, etc even though there are clear rules for this.

If I stumble upon a book that means 1/sin with sin-1, I'll let you know.

I'm quite sure there must be some, otherwise it would be very strange if we both tought that (my chef is a lot older than me, had a different education and has seen more than his share of books; I am just a beginner :))

[hhEb09'1]

With "my old math book" I literally meant mine, not as a general rule for any math book :).I understood that.If I stumble upon a book that means 1/sin with sin-1, I'll let you know.That was my point about your old math book. It didn't necessarily use that. Who wrote it?

[Nicolas]

I can't check that now, it's in my archive in Belgium. However, it's a Belgian (or Dutch) book, and I don't think it's been translated and spread elsewhere.

But there must be more books than just that one that use sin^-1 to indicate 1/sin, otherwise my chef wouldn't also assume that. He used different math books during his education, as the series I used wasn't around back then. Maybe he used the same books as I did on University, but I can't remember those books using sin^-1 for 1/sin. I'm not sure on that though.

I must say that a physics book that uses t for static temperature rather than time is far more confusing for me though :).

[yaohua2000]

After reading this:

http://en.wikipedia.org/wiki/NPOV

I believe it should be ''e''.

[frogesque]

Log(x) is base 10: Ln(x) is the 'natural' base, e.

[Peter Wilson]

Isn't it fun that

loge10 = logx10/logxe

Heh heh, I've never got over that.

clop
Try this one on for size: 2 x 2 = 2 + 2!

[hhEb09'1]

loge10 = logx10/logxe
Not only that, but for almost any a, b, c:

logab = logcb/logca

Because

b = b

alogab = b

(clogca)logab = b

c(logca)(logab) = clogcb

(logca)(logab) = logcb

logab = logcb/logca

(And you thought the BAUT was safe from proofs)

[HenrikOlsen]

Isn't it fun that

loge10 = logx10/logxe

Heh heh, I've never got over that.

clop

The one I always enjoy is eiπ=-1.

[Nicolas]

That one indeed is marvellous.

[crosscountry]

ln is natural log