Log and Ln

Rapid_W · #1 $Old$ August 19th, 2009, 04:19 AM

Why is it that maths lecturers always write log, even though ln is easier to write and has no chance of being confused by a non-maths students such as a physics student where log10 is found a lot more commonly, it's almost as if maths people look down on physics people and just expect them to obey to their rules. I also noticed engineers use j for complex numbers, not sure who is in the wrong there though.

As I have only finished 1st year I am still left feeling a bit awkward when I see log. Do they mean loge or log10, obviously as i am doing maths they always mean ln, but my physics background just makes me feel uneasy.

So where has the maths ego come from? How long has this tradition of calling ln, log, been around for?

pickslides · #2 $Old$ August 19th, 2009, 04:54 AM

In my experience someone writing just $\log$ is incomplete. I do know most calculators have a $\log$ button which implies base 10. When solving a problem using $\log$ this should have the base stated. The only exception is $\ln$ which implies $\log_e$

As far as 'ego' goes I think you are confusing that with precision. Mathematicians can be very meticulous when following certain guidelines. Mathematics has a certain elegance to it.

If you have a lecturer that has a big ego please do not that be a reflection on the rest of the mathematicians around the world.

Opalg · #3 $Old$ August 19th, 2009, 05:49 AM

Quote:

Originally Posted by Rapid_W $View Post$

Why is it that maths lecturers always write log, even though ln is easier to write and has no chance of being confused by a non-maths students such as a physics student where log10 is found a lot more commonly, it's almost as if maths people look down on physics people and just expect them to obey to their rules. I also noticed engineers use j for complex numbers, not sure who is in the wrong there though.

As I have only finished 1st year I am still left feeling a bit awkward when I see log. Do they mean loge or log10, obviously as i am doing maths they always mean ln, but my physics background just makes me feel uneasy.

So where has the maths ego come from? How long has this tradition of calling ln, log, been around for?

There's nothing "right" or "wrong" about differing notations. They are just a matter of convention. For example, electrical engineers find it convenient to use j rather than i for $\sqrt{-1}$ because they normally use i to denote current.

As for "this tradition of calling ln, log", it's actually the other way round. The ln notation was apparently first used in 1893 (by a professor of mathematics in Berkeley), but it was very slow to catch on. I don't remember ever seeing it when I was in school (50 years ago), and I suspect that it only really became popular with the advent of hand-held electronic calculators around 1970. Until then the notation log was nearly always used.

For more information on this, see the Wikipedia Logarithm page.

QM deFuturo · #4 $Old$ August 19th, 2009, 02:24 PM

I don't know how they teach it now, but when I was in school "log" by itself was understood to be the "common" log, i.e., base 10.

"ln" meant "natural log", i.e., log to base e.

And there seemed to be no confusion for me.

However, as a software developer, I have a standing complaint (made only to myself

) in the Java Math libraries, where the Math.log() function is really the NATURAL log, not log to base 10. That causes all kinds of confusion for new programmers using that library, and it caused me confusion until I understood it was base e, not base 10. This is an example of bad API design - don't go against such an established convention. They should have called that method Math.ln(). But they didn't ask my opinion at the time

CaptainBlack · #5 $Old$ August 19th, 2009, 03:18 PM

Quote:

Originally Posted by QM deFuturo $View Post$

I don't know how they teach it now, but when I was in school "log" by itself was understood to be the "common" log, i.e., base 10.

"ln" meant "natural log", i.e., log to base e.

And there seemed to be no confusion for me.

However, as a software developer, I have a standing complaint (made only to myself

) in the Java Math libraries, where the Math.log() function is really the NATURAL log, not log to base 10. That causes all kinds of confusion for new programmers using that library, and it caused me confusion until I understood it was base e, not base 10. This is an example of bad API design - don't go against such an established convention. They should have called that method Math.ln(). But they didn't ask my opinion at the time

In virtually all (Ok in the majority of those I know) programming languages log denotes the natural log.

CB

Jameson · #6 $Old$ August 19th, 2009, 03:21 PM

Here's my experience with schooling in the US:

High School - log is base 10, ln is base e
College - Calculus courses: same thing
Post-calculus: log means natural log.

---
Many upper level math books I have seen use log for ln. It can be weird for a moment trying to figure out which notation is being used.

Swlabr · #7 $Old$ August 20th, 2009, 09:50 AM

As one of my lecturers once said,

"Of course, since you're mathematicians, you should all write $\text{log}_n$ as opposed to $\text{ln}$ . Don't let your boyfriend or girlfriend catch you writing $\text{ln}$ . I had a girlfriend once, a physicist who wrote $\text{ln}$ . We broke up. It wasn't because of that."

Pause, class titters.

"Well, maybe it was."

But then, this was the same man who warned us that the chalk would explode if we divided by zero, and indeed apparently his mother warned him of two things: ladies of a certain virtue, and dividing by zero.