ln(x) or log(x)?

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

User avatar
Mike_Bson
Posts: 252
Joined: Mon Jul 12, 2010 12:00 pm UTC

ln(x) or log(x)?

Postby Mike_Bson » Sat Dec 18, 2010 1:21 am UTC

Note- This seems like the thing that there would probably be another older thread on, but my searching results turned out to be inconclusive. If this is a repeat post, I apologize.

After getting in a multitude of debacles on this, I have decided to seek our the XKCD fora for their views. So, I ask you all: to denote a logarithm to the base e, which to you prefer: log(x), or ln(x)? Personally, I write log(x), in fact, I cringe whenever I see ln(x). This is mostly because I have never ever seen a log to the base 10 used anywhere, so having log(x) mean base 10 by default is pretty silly. It also looks much more elegant to use log(x) as base e, and logb(x) as a logarithm to the base b. What do you guys think?

B.Good
Posts: 271
Joined: Fri Jun 04, 2010 9:34 pm UTC
Location: Maryland

Re: ln(x) or log(x)?

Postby B.Good » Sat Dec 18, 2010 1:42 am UTC

I'm the exact opposite of you, I cringe every time I see log(x) to denote ln(x), it has been drilled into my head to mean "log base 10". Although log base 10 is rare they are used in chemistry to determine the pH of a substance, and I would bet that there are other uses though I am unfamiliar with them, granted, log base e is far more common. Also, I think ln(x) looks much nicer than log(x) and it takes less time to write than log base e, or even log for that matter.

User avatar
greeniguana00
Posts: 113
Joined: Sun Mar 30, 2008 12:09 am UTC
Location: Albany, NY, USA

Re: ln(x) or log(x)?

Postby greeniguana00 » Sat Dec 18, 2010 1:42 am UTC

In middle school, I was taught log(x) in terms of base 10. Only later did I learn about e and its significance.

We were taught that was because it keeps the numbers in calculations nice, and helps you build an intuition for it. For example:

10^0=1
10^1=10
10^2=100
10^3=1000
...
10^k = 100...000 (k zeros)

Then you can approximate (within +/-1) the logarithm of any number in base 10.

For example: What is log(723590943)?

If log is taken base 10, then we know it's between 8 and 9.

More important, it's easy to see that the rules of logarithm work:

3 = log(1000) = log(10*10*10) = log(10)+log(10)+log(10) = 1+1+1 = 3.

If we have a logarithm table for 0 up to 10, we can use these rules to calculate log for for any positive number, no matter how large! Example:
log(723590943645) = log(7.23590943645*10^11) = log(7.23590943645)*log(10^11) = 11*log(7.23590943)

If you work with log base e, you don't have all these nice properties, and the intuition is less clear when learning it for the first time.
Goodnight, g♥♥dnight! There's something magnificent about good night with two disemboweled hearts in it, or at least it seems that way when you're so happy.

User avatar
Mike_Bson
Posts: 252
Joined: Mon Jul 12, 2010 12:00 pm UTC

Re: ln(x) or log(x)?

Postby Mike_Bson » Sat Dec 18, 2010 1:45 am UTC

greeniguana00 wrote:If you work with log base e, you don't have all these nice properties, and the intuition is less clear when learning it for the first time.

Or just write log10(x) when teaching kids about logarithms to build this intuition. In fact, that seems like such a trivial matter, it shouldn't have anything to do with this, and I doubt it does.

User avatar
greeniguana00
Posts: 113
Joined: Sun Mar 30, 2008 12:09 am UTC
Location: Albany, NY, USA

Re: ln(x) or log(x)?

Postby greeniguana00 » Sat Dec 18, 2010 1:59 am UTC

Mike_Bson wrote:
greeniguana00 wrote:If you work with log base e, you don't have all these nice properties, and the intuition is less clear when learning it for the first time.

Or just write log10(x) when teaching kids about logarithms to build this intuition. In fact, that seems like such a trivial matter, it shouldn't have anything to do with this, and I doubt it does.


In complex analysis, the complex logarithm is defined using the real logarithm, i.e. Log z := ln r + iθ = ln | z | + iArg z

So it makes sense to use ln for the (more restricted) real logarithm, and log for the extended complex logarithm.

e is really only beautiful in complex analysis anyway.

Then there is also no problem is defining log to be base 10 as people are introduced to it.

Using log to mean base 10 (except in complex) and ln to mean natural log is the most unambiguous way to do it.
Goodnight, g♥♥dnight! There's something magnificent about good night with two disemboweled hearts in it, or at least it seems that way when you're so happy.

User avatar
Mike_Bson
Posts: 252
Joined: Mon Jul 12, 2010 12:00 pm UTC

Re: ln(x) or log(x)?

Postby Mike_Bson » Sat Dec 18, 2010 2:04 am UTC

greeniguana00 wrote:In complex analysis, the complex logarithm is defined using the real logarithm, i.e. Log z := ln r + iθ = ln | z | + iArg z

I am a noob to complex analysis. Would you kindly inform me the difference of saying Log(z) and ln(r)? Like, I know the former is the log of a complex number, and the latter real, but why use different notation for them? Doesn't it make sense to say ln(z) = ln(r) + iθ +2πik, if we're using ln(x) as the natural logarithm of x?
Using log to mean base 10 (except in complex) and ln to mean natural log is the most unambiguous way to do it.
I disagree. With everyone disagreeing on the definition, log(x) is definitely not unambiguous. Every textbook I've seen, it used ln(x) as the natural log (most likely to cater to non-mathematicians), and log10(x) as the base 10 log.

skullturf
Posts: 556
Joined: Thu Dec 07, 2006 8:37 pm UTC
Location: Chicago
Contact:

Re: ln(x) or log(x)?

Postby skullturf » Sat Dec 18, 2010 2:32 am UTC

My personal preference is for log(x) to mean the natural log. But when teaching calculus, I defer to all the textbooks, and use ln.

In a more specialized academic context -- writing a research article, or giving a presentation to fellow PhDs -- I would use "log" to mean the natural log. (Possibly I would include a brief remark to that effect at the beginning.) I should point out that I'm in math (probability, classical analysis, and such) -- chemists or earth scientists, say, might understandably have a different convention.

Two aesthetic flaws that "ln" has, in my opinion:

-- The lower case L looks like a capital i. "ln" looks like "In". I've noticed that students, especially some whose native language doesn't use our alphabet, make the mistake of writing it as "In".

-- How do you pronounce "ln"? I grew up calling it "lawn" or "lon" (I grew up in a place where "don" and "dawn" are homophones, which isn't true everywhere). I've also heard "lin" and "ell en". Lately, I prefer "ell en", but I think all the possibilities sound a little awkward or dorky. (I realize personal aesthetics are subjective, though.)

++$_
Mo' Money
Posts: 2370
Joined: Thu Nov 01, 2007 4:06 am UTC

Re: ln(x) or log(x)?

Postby ++$_ » Sat Dec 18, 2010 2:39 am UTC

I pronounce it "log."

I pretty much write "log" for the natural log, except when teaching non-math people, when I use "ln" because they seem to like it that way. (Also, the TI calculators say "LN" on the log button and "LOG" on the log10 button, so if I use "log" when teaching I find that the students are likely to push the wrong button at some point and get confused.)

If I have to use a log base 2, I would just write that log2 ("lg" is an abomination because it is not pronounced differently from "log"). I almost never have to use log base 10 or anything else, but I'd do those the same way.

User avatar
greeniguana00
Posts: 113
Joined: Sun Mar 30, 2008 12:09 am UTC
Location: Albany, NY, USA

Re: ln(x) or log(x)?

Postby greeniguana00 » Sat Dec 18, 2010 3:36 am UTC

Mike_Bson wrote:
greeniguana00 wrote:In complex analysis, the complex logarithm is defined using the real logarithm, i.e. Log z := ln r + iθ = ln | z | + iArg z

I am a noob to complex analysis. Would you kindly inform me the difference of saying Log(z) and ln(r)? Like, I know the former is the log of a complex number, and the latter real, but why use different notation for them? Doesn't it make sense to say ln(z) = ln(r) + iθ +2πik, if we're using ln(x) as the natural logarithm of x?


Well, first, there is a difference between "log(z)" and "Log(z)". The first is single-valued, but doesn't vary continuously on the complex plane. The second is multi-valued, but can be made to vary continuously.
This difference arises from arg(z) vs. Arg(z). Both measure the "angle" of a complex number, but the angle is really only unique up to multiples of 2pi. (i.e. pi/2 refers to the same angle as pi/2 + 2pi). arg(z) gives you all the numbers that refer to that particular angle, while Arg(z) returns only the number between -pi and pi.

Using "log" to refer to base e is much more natural in the complex numbers, because e is so tied up in the algebra of the complex plane. For example, e^(i*t) = cost + i*sint. Specifically, e^(i*pi) = -1. No one would ever use log base 10 in the complex numbers.

e doesn't really have algebraic properties that interesting in the real numbers, so the natural log and base 10 log both have potential uses. Seeing as both ln and log are used when dealing with real numbers, and seeing as there are people who might use both frequently, it's probably good for there to be an easy distinction between them that doesn't require tedious subscripts.
Goodnight, g♥♥dnight! There's something magnificent about good night with two disemboweled hearts in it, or at least it seems that way when you're so happy.

achan1058
Posts: 1783
Joined: Sun Nov 30, 2008 9:50 pm UTC

Re: ln(x) or log(x)?

Postby achan1058 » Sat Dec 18, 2010 4:37 am UTC

For general purposes, I use log for base 10, ln for base e, and lg for base 2. For field specific purposes, I tend to use log for all, letting people infer from context. Besides, for things like analysis and complexity theory, which base of log often don't matter that much anyways.

Jyrki
Posts: 117
Joined: Mon Dec 06, 2010 12:27 pm UTC
Location: Rusko, Finland

Re: ln(x) or log(x)?

Postby Jyrki » Sat Dec 18, 2010 7:54 am UTC

This is something that we simply have to agree to disagree on. It depends on the field (i.e. context), which base is the most common. The weight of history also comes into play. As do the choices made by the authors of most common textbooks and computer algebra systems.

My personal preference is to always use 'log' with a subscript, 'lg' for base 10, 'ln' for base e, and 'lb' for base 2 (though I might also write log2 for that). But this is just a preference.

If I'm coerced to make a pick, I would prefer 'log' to mean base 10. Admittedly that is because during my formative years calculators where not at all common, so folks learned to work with logarithm tables well before they learned anything about derivatives, and at that point base 10 was the obvious choice. In addition to the pH-scale, base 10 is used in telecommunications, because both error probabilities and signal-to-noise ratios are often described in powers of ten. The former because it is then easy to quickly come up with ball park figures, of how often something goes wrong - the latter because it is measured using the decibel (dB) scale.

Of course, in the context of complex analysis 'log' surely means base e, or rather, (one of the branches of) the inverse of the complex exponential function.

I frankly don't see the point of trying to compress the names of these functions in spoken language. There is usually enough background noise, and my goal is then to minimize the chance of anyone mishearing it. May be my bias to lecture room setting shows here :wink: ? I would simply use phrases like "natural log(arithm)", "Briggs' log" or "log base 10" and "binary log" or "log base 2". In particular when to the chalkboard. The audience immediately also gets an idea of my preferences making communication in the immediate future that much less prone to errors.

That was the tl;dr; version. The summary: it all depends on the context.

forgetful functor
Posts: 10
Joined: Mon Nov 22, 2010 10:40 am UTC

Re: ln(x) or log(x)?

Postby forgetful functor » Sat Dec 18, 2010 8:51 am UTC

Once you get past introductory calculus classes, there is pretty much universal agreement in math that log means the "natural" or "base-e" logarithm. In fact, I don't recall ever seeing "ln" in any math textbook beyond the calculus level.

User avatar
314man
Posts: 119
Joined: Sat Oct 09, 2010 6:03 pm UTC
Location: Ontario

Re: ln(x) or log(x)?

Postby 314man » Sat Dec 18, 2010 9:13 am UTC

I've always learned that ln is base e and log is base 10. I see that almost 100% of the time. I notice my current (well the final was today so not current anymore) calc prof says "log" for the natural log. I'm only a 2nd year university student so I don't know if the textbooks and profs start switching to log.

Personally I think it should be as how I see it because almost everyone first learns logarithms in base 10, and it's hard for people to lose their habits. It's especially important for teachers because they throw around 'log' and it takes students a while to get that he/she means the natural log.

Also ln is shorter to write than log which is never a bad thing haha

User avatar
NathanielJ
Posts: 882
Joined: Sun Jan 13, 2008 9:04 pm UTC

Re: ln(x) or log(x)?

Postby NathanielJ » Sat Dec 18, 2010 3:17 pm UTC

Relevant thread

And I use ln(x) for base e since that's just what I see most frequently used.
Homepage: http://www.njohnston.ca
Conway's Game of Life: http://www.conwaylife.com

///
Posts: 3
Joined: Tue Sep 21, 2010 5:01 pm UTC

Re: ln(x) or log(x)?

Postby /// » Sat Dec 18, 2010 11:01 pm UTC

I usually prefer ln(x) as logarithm to the base e and log(x) to the base 10.

User avatar
Diadem
Posts: 5654
Joined: Wed Jun 11, 2008 11:03 am UTC
Location: The Netherlands

Re: ln(x) or log(x)?

Postby Diadem » Sun Dec 19, 2010 12:46 am UTC

In my experience mathematicians seem to prefer log and physicists seem to prefer ln. Theoretical physicists (being closer to mathematicians) seem divided on the issue. But certainly none of them would ever mistake log(x) for log10(x). And no mathematician would fail to understand the meaning of ln(x). So there's not really a problem.

I myself use log. I actually consciously made that choice as a way of saying "I may be a physicist, but I do enjoy mathematics a lot".
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
- Bernard Woolley in Yes, Prime Minister

User avatar
Mike_Bson
Posts: 252
Joined: Mon Jul 12, 2010 12:00 pm UTC

Re: ln(x) or log(x)?

Postby Mike_Bson » Sun Dec 19, 2010 12:49 am UTC

Diadem wrote:I actually consciously made that choice as a way of saying "I may be a physicist, but I do enjoy mathematics a lot".

I said something like, ''I don't give a damn about base 10, so I won't dignify it by saying ln.''

User avatar
Eastwinn
Posts: 303
Joined: Thu Jun 19, 2008 12:36 am UTC
Location: Maryland

Re: ln(x) or log(x)?

Postby Eastwinn » Sun Dec 19, 2010 3:00 am UTC

I alternate between them. :D
http://aselliedraws.tumblr.com/ - surreal sketches and characters.

User avatar
Wnderer
Posts: 640
Joined: Wed Feb 03, 2010 9:10 pm UTC

Re: ln(x) or log(x)?

Postby Wnderer » Sun Dec 19, 2010 4:48 pm UTC

That's what's wrong with you kids today. Saying log(x) has base e. :roll: Haven't you heard of sliderules and log-log and semilog graph paper or decibels? Let say you only have regular graph paper to graph your log curve. Well if you know that the log(2) ~= 0.3, and the log(pi) ~=0.5, you can make your graph. So for every 10 ticks, 1 at 0, 2 at 3, 4 at 6, 8 at 9 and pi at 5. Just scale them by tens for what ever scale you need. No you kids need a super computer to do anything.

david.lewis314
Posts: 1
Joined: Mon Dec 20, 2010 3:09 am UTC

Re: ln(x) or log(x)?

Postby david.lewis314 » Mon Dec 20, 2010 3:28 am UTC

When studying calculus in high school we wrote ln for natural logarithm. However, while doing maths at university we tended to use log to indicate the natural logarithm, although some lecturers still preferred to write ln. I think that if you wrote log in the context of a maths paper, people would assume you meant the natural logarithm, but ln would still be understood. I did get the impression that some people regarded writing ln as something not done by 'real mathematicians', but that was just an impression.

Tetra
Posts: 2
Joined: Mon Apr 30, 2007 6:23 pm UTC

Re: ln(x) or log(x)?

Postby Tetra » Mon Dec 20, 2010 4:02 am UTC

Student in my class: So you're using "log" for the natural log?
Physics professor: I don't know of any other kind.

User avatar
phlip
Restorer of Worlds
Posts: 7572
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

Re: ln(x) or log(x)?

Postby phlip » Mon Dec 20, 2010 4:24 am UTC

I think it's similar to degrees/radians... when first teaching trig, everything's done in degrees, because that's what the students would be familiar with. Trying to introduce radians at this point would just result in a lot of "but... why?". But then when you get to calculus, or complex numbers, the advantages of radians become apparent. People will still use degrees over radians colloquially, and in fields other than pure maths (physics et al) but within maths, it's typically assumed to be radians.

Similarly for logs... when first teaching them, everything's in decimal, 'cause that's what the students are familiar with. But later, in calculus, the value of e is actually relevant, and the natural log is useful.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

User avatar
Diadem
Posts: 5654
Joined: Wed Jun 11, 2008 11:03 am UTC
Location: The Netherlands

Re: ln(x) or log(x)?

Postby Diadem » Mon Dec 20, 2010 12:57 pm UTC

Wnderer wrote:That's what's wrong with you kids today. Saying log(x) has base e. :roll: Haven't you heard of sliderules and log-log and semilog graph paper or decibels? Let say you only have regular graph paper to graph your log curve. Well if you know that the log(2) ~= 0.3, and the log(pi) ~=0.5, you can make your graph. So for every 10 ticks, 1 at 0, 2 at 3, 4 at 6, 8 at 9 and pi at 5. Just scale them by tens for what ever scale you need. No you kids need a super computer to do anything.

Wait. Why would I want to do something as crazy as actually calculating a result in the first place? What do you take me for? An experimental physicist?
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
- Bernard Woolley in Yes, Prime Minister

User avatar
mister k
Posts: 643
Joined: Sun Aug 27, 2006 11:28 pm UTC
Contact:

Re: ln(x) or log(x)?

Postby mister k » Mon Dec 20, 2010 1:59 pm UTC

log is base e, because I want to be differentiating. and having bases other than e makes my life more complicated. I don't think you'll find a statistician who'll do it any other way.
Elvish Pillager wrote:you're basically a daytime-miller: you always come up as guilty to scumdar.

User avatar
314man
Posts: 119
Joined: Sat Oct 09, 2010 6:03 pm UTC
Location: Ontario

Re: ln(x) or log(x)?

Postby 314man » Mon Dec 20, 2010 8:56 pm UTC

phlip wrote:I think it's similar to degrees/radians... when first teaching trig, everything's done in degrees, because that's what the students would be familiar with. Trying to introduce radians at this point would just result in a lot of "but... why?". But then when you get to calculus, or complex numbers, the advantages of radians become apparent. People will still use degrees over radians colloquially, and in fields other than pure maths (physics et al) but within maths, it's typically assumed to be radians.

Similarly for logs... when first teaching them, everything's in decimal, 'cause that's what the students are familiar with. But later, in calculus, the value of e is actually relevant, and the natural log is useful.



I get what you're saying, although there is a difference. Degrees/Radians actually gives different answers when calculating. When doing trig functions by itself, there is no real clear advantage. But if you have a function like xsinx, there is a huge difference between degrees and radians. On the other hand, there is no difference between using ln and log (in base e of course) other than how it looks visually or pronounced

User avatar
phlip
Restorer of Worlds
Posts: 7572
Joined: Sat Sep 23, 2006 3:56 am UTC
Location: Australia
Contact:

Re: ln(x) or log(x)?

Postby phlip » Mon Dec 20, 2010 10:55 pm UTC

I wasn't presenting it as a difference between "log(x)" (implied base e) and "ln(x)", but as a difference between "log(x)" (implied base e) and "log(x)" (implied base 10).

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

User avatar
Mike_Bson
Posts: 252
Joined: Mon Jul 12, 2010 12:00 pm UTC

Re: ln(x) or log(x)?

Postby Mike_Bson » Mon Dec 20, 2010 11:34 pm UTC

phlip wrote:I think it's similar to degrees/radians... when first teaching trig, everything's done in degrees, because that's what the students would be familiar with. Trying to introduce radians at this point would just result in a lot of "but... why?". But then when you get to calculus, or complex numbers, the advantages of radians become apparent. People will still use degrees over radians colloquially, and in fields other than pure maths (physics et al) but within maths, it's typically assumed to be radians.

Similarly for logs... when first teaching them, everything's in decimal, 'cause that's what the students are familiar with. But later, in calculus, the value of e is actually relevant, and the natural log is useful.

Plus ln notation and degrees are also similar in the sense that neither of them should ever be used :D .
Last edited by Mike_Bson on Wed Dec 22, 2010 4:27 am UTC, edited 1 time in total.

User avatar
Dopefish
Posts: 855
Joined: Sun Sep 20, 2009 5:46 am UTC
Location: The Well of Wishes

Re: ln(x) or log(x)?

Postby Dopefish » Tue Dec 21, 2010 12:35 am UTC

I like ln(x) myself. Less writing, and I don't think theres any amibiguity like with log(x).

If I encounter log(x), if I don't automatically know from context (which I usually do), I'll either plug in log(10) to see if I get 1 or some decimal (when I encounter it within a program for example), or if it's in a book I'll hunt around until I can find an example where it's clearly base e (or base 10), and use that as that standard for the remainder of the book.

User avatar
314man
Posts: 119
Joined: Sat Oct 09, 2010 6:03 pm UTC
Location: Ontario

Re: ln(x) or log(x)?

Postby 314man » Tue Dec 21, 2010 1:29 am UTC

phlip wrote:I wasn't presenting it as a difference between "log(x)" (implied base e) and "ln(x)", but as a difference between "log(x)" (implied base e) and "log(x)" (implied base 10).


oh right, my bad. I should've read your post more carefully

capefeather
Posts: 98
Joined: Sun Dec 14, 2008 4:23 am UTC

Re: ln(x) or log(x)?

Postby capefeather » Sat Dec 25, 2010 11:14 pm UTC

I don't think that notations should be personally adopted on the basis of some kind of elitist mentality, as it seems to be in this case. I honestly prefer ln just because it's less ambiguous, but when I write log I typically mean the natural log, too. I'm not all that consistent, and I tend to adopt the notations of whatever math profs I have at the time, but absolute consistency got overrated ever since we needed more than 52 constants. It doesn't really matter with ln/log, but with degrees/radians, it is often better to use degrees in non-math-related contexts because they're better for actually measuring, which is KIND OF important for applying our math to real world situations. It's "nice" in that context to have a full revolution represented by an algebraic number - a NATURAL number, even.

dag618
Posts: 4
Joined: Sun Nov 08, 2009 8:35 pm UTC

Re: ln(x) or log(x)?

Postby dag618 » Sun Jan 02, 2011 12:41 am UTC

I was always taught that log(x) is log base 10 of x and ln(x) is log base e of x. It would get confusing, especially to an engineer like myself, when it comes to things like http://en.wikipedia.org/wiki/Decibel since very few engineers will always specify the base of the log.

Nic the Man
Posts: 22
Joined: Fri Apr 30, 2010 4:14 am UTC

Re: ln(x) or log(x)?

Postby Nic the Man » Mon Jan 03, 2011 5:19 am UTC

On the topic of engineers, I'd be curious to hear stories of some sort of construction failure due to someone down the line mistaking log 10 with log e. It would not surprise me.

Personally, I'm a log = 10, ln = e, lg = 2. But it's all very contextual. If I'm doing CS work, nearly every logarithm is base 2 so "log = lg = log2". Whereas in the mathematics realm, log = ln = loge. If I'm in the engineering realm, and (Much to the chagrin of some of my professors), ln.

Plus, I've always learned to hand-write the ln with a curly lower-case l just to differentiate it from the capital i. So I like curly.

User avatar
Talith
Proved the Goldbach Conjecture
Posts: 848
Joined: Sat Nov 29, 2008 1:28 am UTC
Location: Manchester - UK

Re: ln(x) or log(x)?

Postby Talith » Mon Jan 03, 2011 5:00 pm UTC

I wonder if the use of i instead of j for complex numbers has ever caused a transformer station to blow up or something... (cos if it hasn't then they should stop using j dammit! :) )

User avatar
yeyui
Posts: 102
Joined: Sun Sep 16, 2007 10:45 pm UTC
Location: Kinston, NC, USA
Contact:

Re: ln(x) or log(x)?

Postby yeyui » Mon Jan 03, 2011 9:09 pm UTC

It doesn't really matter with ln/log, but with degrees/radians, it is often better to use degrees in non-math-related contexts because they're better for actually measuring, which is KIND OF important for applying our math to real world situations. It's "nice" in that context to have a full revolution represented by an algebraic number - a NATURAL number, even.


Yeah... ::sarcastic sigh:: You just calibrate your protractor to read from 0 to 2 (2=two half revolutions), then use [imath]\pi[/imath] the same way your would use [imath]^\circ[/imath] ---as a unit.


Actually, I prefer to measure angles so that the winding number is equal to the angle measure (angle of measure 1 is one full rotation). If I want finer resolution to my measurements, I am fully capable of using rational numbers. Dividing the circle into 360 parts seems so excessing, and [imath]2\pi[/imath] parts so messy (unless you are calculating arclength!), but letting a circle be unity---Ah! now that is beautiful.

User avatar
Talith
Proved the Goldbach Conjecture
Posts: 848
Joined: Sat Nov 29, 2008 1:28 am UTC
Location: Manchester - UK

Re: ln(x) or log(x)?

Postby Talith » Mon Jan 03, 2011 9:19 pm UTC

Well you're more likely to be working with a circle of radius 1 as opposed to a circle with circumference 1 and I'd much rather have 2pi radians circumference than have a circle of 0.5(pi)^-1 radius.

User avatar
Eebster the Great
Posts: 3459
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: ln(x) or log(x)?

Postby Eebster the Great » Thu Jan 06, 2011 11:41 pm UTC

There are plenty of practical applications of base ten logs for the obvious reason that we use a base ten number system. So it shows up in logarithmic scales like pH, sound intensity (bels), and the Richter's scale. There are plenty of practical and theoretical applications of base e logs for reasons obvious to anyone who has taken calculus.

Wouldn't it be great if we could distinguish between these on paper?

Reference two for why I use ln(x) for loge x: my TI calculator.


But in all seriousness, how often does this actually cause confusion? It seems like it should generally be pretty obvious from the context.


Oh, and I pronounce "ln(x)" exactly like that, "the el en of ex" (or just "el en ex"). Or "log" if I'm lazy :).


E: Oh yeah, and replacing "i" with "j" for complex numbers is seriously confusing. My mind always does something like, "wait, this is a vector? No, no, that's not a unit vector and they're adding it to a scalar. But they never defined the variable, and there's no index . . . Oh shit, these aren't quaternions are they? I've never used those. No, that would be weird. Oh shit, they're electrical engineers." Some physicists do this too. Very annoying.

micawber
Posts: 2
Joined: Thu Jan 06, 2011 10:24 pm UTC

Re: ln(x) or log(x)?

Postby micawber » Thu Jan 06, 2011 11:45 pm UTC

The only time where I have ever seen this cause confusion in practice is in numerical calculations; bizarrely, Microsoft Excel uses log() for the base-10 log but VBA uses log() for the natural log. So switching back and forth from one to the other can cause errors.

User avatar
Dopefish
Posts: 855
Joined: Sun Sep 20, 2009 5:46 am UTC
Location: The Well of Wishes

Re: ln(x) or log(x)?

Postby Dopefish » Fri Jan 07, 2011 8:07 pm UTC

Eebster the Great wrote:E: Oh yeah, and replacing "i" with "j" for complex numbers is seriously confusing. My mind always does something like, "wait, this is a vector? No, no, that's not a unit vector and they're adding it to a scalar. But they never defined the variable, and there's no index . . . Oh shit, these aren't quaternions are they? I've never used those. No, that would be weird. Oh shit, they're electrical engineers." Some physicists do this too. Very annoying.


Yeah, the whole j thing seems completely unnecessary (and something I don't use, as my knowledge of the subject comes form physics). Sure capital i is current, but i and I are pretty distinct. Besides that, in an electrical context, capital (vector) J I was taught to mean volume current density anyway, so theres still potential ambiguity, if not more so since j and J are probably easier to confuse imo. Never mind that J could be the unit joule, which also has potential to pop up in electrical problems (although I don't know what the engineers are doing).

User avatar
Eebster the Great
Posts: 3459
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: ln(x) or log(x)?

Postby Eebster the Great » Sat Jan 08, 2011 12:46 am UTC

Dopefish wrote:
Eebster the Great wrote:E: Oh yeah, and replacing "i" with "j" for complex numbers is seriously confusing. My mind always does something like, "wait, this is a vector? No, no, that's not a unit vector and they're adding it to a scalar. But they never defined the variable, and there's no index . . . Oh shit, these aren't quaternions are they? I've never used those. No, that would be weird. Oh shit, they're electrical engineers." Some physicists do this too. Very annoying.


Yeah, the whole j thing seems completely unnecessary (and something I don't use, as my knowledge of the subject comes form physics). Sure capital i is current, but i and I are pretty distinct. Besides that, in an electrical context, capital (vector) J I was taught to mean volume current density anyway, so theres still potential ambiguity, if not more so since j and J are probably easier to confuse imo. Never mind that J could be the unit joule, which also has potential to pop up in electrical problems (although I don't know what the engineers are doing).

lowercase i is frequently used to represent current, though. Sometimes you will see capital I used as a constant and lowercase i used as a variable, or sometimes they will be used in different contexts, or sometimes i will be complex current and I will be the real part.

Yeah, it actually seems like EE are pretty big on ambiguity . . .


Oh, and j as the complex unit still isn't as annoying as the cgs system. God converting between systems is a nightmare.

User avatar
kernelpanic
Posts: 891
Joined: Tue Oct 28, 2008 1:26 am UTC
Location: 1.6180339x10^18 attoparsecs from Earth

Re: ln(x) or log(x)?

Postby kernelpanic » Sat Jan 08, 2011 3:15 am UTC

I use log to mean base 10 and ln for e. This is because I use ln more commonly, and it's a bit shorter. (Yes, I'm that lazy)
I'm not disorganized. My room has a high entropy.
Bhelliom wrote:Don't forget that the cat probably knows EXACTLY what it is doing is is most likely just screwing with you. You know, for CAT SCIENCE!

Image


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 7 guests