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[Witherweaver]

....

Like I said, bespoke interests.  Not a natural definition at all.

[silverspawn]

I mean using "ln" is okay, that's not the point.  The point is that ln = log.

Saying "log(x)" and meaning a base that is not e is misleading and should be avoided.

You're hardly ever going to need base 10 or base 2 or base pi, so in those cases just write log_10(x), log_2(x), log_pi(x).  Easy.

but that's not true. you need ld. lots of sorting algorithms have ld(n) * n * c

I'm right!!!

ftfy
；）

[pingpongsam]

Conclusion:  Mathematicians are out of touch with how math is actually used throughout life.

Oh please.  In any reasonable definition of "real life", logarithms aren't used at all.

I use logs normally.  My life is real.

Nah, it's an approximation quantized to sufficient resolution that you cannot discern the difference.

[LastFootnote]

....

Like I said, bespoke interests.  Not a natural definition at all.

Ha ha! So the reason that your default is the "natural" default is because you say so. Everybody else's extremely common uses of logarithms are strange edge cases to you. What?

[Witherweaver]

No, it's natural in the sense that y(x) =e^x solves

y' = y

with y(0) = 1

[Witherweaver]

Whereas y = b^x solves

y' = log(b)*y

with y(0) = 1. 

Which ODE is most natural?  y' = y or y' = log(b)y? 

[silverspawn]

something different... my ears are itchy, I've been scratching them way too much and they keep getting more itchy. this is bad.

[SirPeebles]

....

Like I said, bespoke interests.  Not a natural definition at all.

Ha ha! So the reason that your default is the "natural" default is because you say so. Everybody else's extremely common uses of logarithms are strange edge cases to you. What?

Using logarithm base 10 is a lot like measuring angles in degrees.  They sync up nicely with conventions that humans hit upon for convenience and are therefore often used when presenting results.  But whether you are a mathematician, engineer, scientist, programmer, or financial analyst you are going to reach for logarithm base e and measure your angles in radians whenever you do any reasonably in depth analysis.  Logarithm base 10 is just too cumbersome.  It's not quite as bad as using Roman numerals over Arabic (Hindu) numerals, but it's still awkward.  (In light of complex analysis, there is a sense in which choosing base e is the same thing as choosing radians)

[sudgy]

In my experience from uni:

Mathematicians and (most) scientists use log to mean natural log
Engineers use log to mean base 10
Programmers and Computer Scientists use log to mean base 2

I don't know about other fields of study, but here in the UK you learn log is base 10 during A level and ln is base e (and most calculators are made the same way)

So basically it sounds like log is a general designation for logarithm that has different default bases depending on the field you're in.

In order to teach the concept, schools start off with base 10, which is reasonable since many students don't even know about the existence of e yet. Once you get into a field that uses logarithms, then people bypass the more wordy "log in base x" and just use "log" with the understanding that your colleague knows that it's in base x. Good to know.

My textbook was talking about logs for the first time, and it first said you can use any base.  It then instantly proceeded to say that log by itself is base 10, and that ln is base e (and that was the first time it introduced e, saying that it is an important number in calculus).

[Kirian]

Conclusion:  Mathematicians are out of touch with how math is actually used throughout life.

Oh please.  In any reasonable definition of "real life", logarithms aren't used at all.

Let me rephrase, then.  Among people who use logarithms, use of the base-10 logarithm is more common than use of the natural logarithm.  Or, perhaps:  among people who use scales based on logarithms (pH, dB, O.D., etc) on a regular basis, more use scales based on the common logarithm.

Stated another way:  If you live in a settlement of ~1000 or more, there's a strong chance someone in your town dealt with common logarithms today, either directly or indirectly.

Using logarithm base 10 is a lot like measuring angles in degrees.  They sync up nicely with conventions that humans hit upon for convenience and are therefore often used when presenting results.  But whether you are a mathematician, engineer, scientist, programmer, or financial analyst you are going to reach for logarithm base e and measure your angles in radians whenever you do any reasonably in depth analysis.

I have to strongly disagree.  Engineers don't use radians except for (some) EE's dealing with AC power.  Nobody is going to convert pH measurements into something else, as that would entirely destroy the point of the pH scale.  Obviously I'll spot you mathematicians and financial analysts.

Interestingly, your categorization of people who might use logarithms betrays biases I hadn't really thought of.  The category 'mathematicians' contains an order of magnitude fewer people than the category 'scientists' even when we only include the natural sciences and ignore the social sciences.

[Kirian]

....

Like I said, bespoke interests.  Not a natural definition at all.

Ha ha! So the reason that your default is the "natural" default is because you say so. Everybody else's extremely common uses of logarithms are strange edge cases to you. What?

No, I think this point should be conceded; I mean, there's a very good reason we call it the 'natural logarithm.'  The number e comes directly from simple mathematical relationships, much as tau does.

[Witherweaver]

In my experience from uni:

Mathematicians and (most) scientists use log to mean natural log
Engineers use log to mean base 10
Programmers and Computer Scientists use log to mean base 2

I don't know about other fields of study, but here in the UK you learn log is base 10 during A level and ln is base e (and most calculators are made the same way)

So basically it sounds like log is a general designation for logarithm that has different default bases depending on the field you're in.

In order to teach the concept, schools start off with base 10, which is reasonable since many students don't even know about the existence of e yet. Once you get into a field that uses logarithms, then people bypass the more wordy "log in base x" and just use "log" with the understanding that your colleague knows that it's in base x. Good to know.

My textbook was talking about logs for the first time, and it first said you can use any base.  It then instantly proceeded to say that log by itself is base 10, and that ln is base e (and that was the first time it introduced e, saying that it is an important number in calculus).

Most math textbooks will use log for base e once you get past high school/freshman level.  In particular, your ODE and PDE books (Gilbarg and Trudinger, for one example).

[sudgy]

In my experience from uni:

Mathematicians and (most) scientists use log to mean natural log
Engineers use log to mean base 10
Programmers and Computer Scientists use log to mean base 2

I don't know about other fields of study, but here in the UK you learn log is base 10 during A level and ln is base e (and most calculators are made the same way)

So basically it sounds like log is a general designation for logarithm that has different default bases depending on the field you're in.

In order to teach the concept, schools start off with base 10, which is reasonable since many students don't even know about the existence of e yet. Once you get into a field that uses logarithms, then people bypass the more wordy "log in base x" and just use "log" with the understanding that your colleague knows that it's in base x. Good to know.

My textbook was talking about logs for the first time, and it first said you can use any base.  It then instantly proceeded to say that log by itself is base 10, and that ln is base e (and that was the first time it introduced e, saying that it is an important number in calculus).

Most math textbooks will use log for base e once you get past high school/freshman level.  In particular, your ODE and PDE books (Gilbarg and Trudinger, for one example).

I have a college calculus textbook that goes all the way up through vector calculus, and it uses ln for natural log the whole time (it rarely ever uses the common log).

[Witherweaver]

Vector calculus is Freshman calculus.

[sudgy]

Vector calculus is Freshman calculus.

They teach that whole book in freshman year, when my brother took several classes through multiple terms and only got about halfway through the book?

[pacovf]

Mathematical conventions

[Serious Cat]

Is serious business.


(sorry for the lack of meme, I'm in a hurry)

[Witherweaver]

Vector calculus is Freshman calculus.

They teach that whole book in freshman year, when my brother took several classes through multiple terms and only got about halfway through the book?

At my school yes.  Plus many students will come in having taken calculus in high school, so "calc 3" will be freshman calc

[enfynet]

So far the best argument is the calculator one. Lets be honest, if you're using a tool like a calculator to solve logarithms then you will normally refer to the written form in the same way. Most calculators have ln and log, meaning natural log and common log, respectively.

[GeoLib]

So far the best argument is the calculator one. Lets be honest, if you're using a tool like a calculator to solve logarithms then you will normally refer to the written form in the same way. Most calculators have ln and log, meaning natural log and common log, respectively.

Mathematica uses Log[x ] to mean natural log of x by default and that's the tool I use to do most of my calculating at this point.

Edit: So apparently brackets makes a bullet point. That is not what I meant to do...

[Witherweaver]

So far the best argument is the calculator one. Lets be honest, if you're using a tool like a calculator to solve logarithms then you will normally refer to the written form in the same way. Most calculators have ln and log, meaning natural log and common log, respectively.

Mathematica uses Log

• to mean natural log of x by default and that's the tool I use to do most of my calculating at this point.

As does Maple, Matlab, and pretty much every calculation tool.  (http://www.mathworks.com/help/matlab/ref/log.html for reference)

That log refers to the natural logarithm is the obvious standard.

[Kirian]

So far the best argument is the calculator one. Lets be honest, if you're using a tool like a calculator to solve logarithms then you will normally refer to the written form in the same way. Most calculators have ln and log, meaning natural log and common log, respectively.

Mathematica uses Log

• to mean natural log of x by default and that's the tool I use to do most of my calculating at this point.

As does Maple, Matlab, and pretty much every calculation tool.  (http://www.mathworks.com/help/matlab/ref/log.html for reference)

That log refers to the natural logarithm is the obvious standard.

...among people who use Matlab, Maple, and Mathematica.  In other words, among mathematicians.

[Witherweaver]

Or as I like to call us, "normal people"

[GeoLib]

So far the best argument is the calculator one. Lets be honest, if you're using a tool like a calculator to solve logarithms then you will normally refer to the written form in the same way. Most calculators have ln and log, meaning natural log and common log, respectively.

Mathematica uses Log

• to mean natural log of x by default and that's the tool I use to do most of my calculating at this point.

As does Maple, Matlab, and pretty much every calculation tool.  (http://www.mathworks.com/help/matlab/ref/log.html for reference)

That log refers to the natural logarithm is the obvious standard.

...among people who use Matlab, Maple, and Mathematica.  In other words, among mathematicians.

I use Mathematica extensively in all of my science courses. I would actually say that it's less useful for mathematicians because it doesn't do the abstract stuff.

(Note that I'm not necessarily arguing that log should mean one thing or the other. I liked the definition from whoever it was that said that the default meaning depends on the field)

[Kuildeous]

I'm bored of this already. Can we get back to Silverspawn's problems?

I saw an article that Weird Al apologized for using "spastic" in a song as a derogatory term. I did not realize that it was an offensive word. It makes sense now, but has the offense factor of this word recently escalated?

[LastFootnote]

I'm bored of this already. Can we get back to Silverspawn's problems?

I saw an article that Weird Al apologized for using "spastic" in a song as a derogatory term. I did not realize that it was an offensive word. It makes sense now, but has the offense factor of this word recently escalated?

For what it's worth, when I heard it in that song, I was surprised. Not personally offended, but surprised. I knew it wasn't politically correct.

EDIT: The Wikipedia article actually talks about this: http://en.wikipedia.org/wiki/Spastic