LOG vs LN

Among mathematicians, log has replaced ln. Among non-mathematicians who use logs for practical purposes (there may be a few such fossils left) and in most high schools, log means log to the base 10.

The reasons are that the natural log is useful all over the place in calculus and that the common log is no longer of much practical use in computation. However, the common log is much easier for beginning students to grasp, which is probably why it has not disappeared from high schools.
 
JeffM said:
Among mathematicians, log has replaced ln. Among non-mathematicians who use logs for practical purposes (there may be a few such fossils left) and in most high schools, log means log to the base 10.

The reasons are that the natural log is useful all over the place in calculus and that the common log is no longer of much practical use in computation. However, the common log is much easier for beginning students to grasp, which is probably why it has not disappeared from high schools.
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I'm a Physicist! Thhhppttt!

I got taught using ln(.) and frankly I'm too crotchety to change. I still use asn(.), too, instead of [math]sin^{-1}(.)[/math], at least in my own hen-scratchings.

Since I'm here and whining about it, what is Math-speak for log base 10?

-Dan
 
topsquark said:
I'm a Physicist! Thhhppttt!

I got taught using ln(.) and frankly I'm too crotchety to change. I still use asn(.), too, instead of [math]sin^{-1}(.)[/math], at least in my own hen-scratchings.

Since I'm here and whining about it, what is Math-speak for log base 10?

-Dan
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Common logarithm. An historic relic from when it was commonly used in hand computation. If you use scientific notation and log tables (as I was taught during the most recent Ice Age when I rode a mammoth to school), conversion to the common log is a snap by hand, to the natural logarithm an utter nightmare.

As far as I am concerned, the elimination of ln is an example of academic imperialism: the greater suppress the lesser while signalling contempt and disdain for their manifest inferiors. It is intellectual Kipling squared.

Oh, and I am such a fossil that I write arcsin.
 
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Yup. No substitute for knowing what one means and failing to assume that everyone means the same thing without explanation.
 
Some here seem to think that this some new to real mathematics education. Not so.. I first encountered it in the late 1960's or early 70's. Leonard Gillman (of Gillam & Jerison fame) Wrote a calculus text using the idea \(L(x) =\displaystyle\int_0^x {\frac{1}{t}dt} \) as the logarithm. Because Prof Gilliam was also president of then MAA it was a natural for the \(\log(x)\) to become the standard notation and once the computer algebra developers picked it up the old notation was doomed. I had many a fight in directors meetings about that usage (chemistry profs are the worst).
 
pka said:
Some here seem to think that this some new to real mathematics education. Not so.. I first encountered it in the late 1960's or early 70's. Leonard Gillman (of Gillam & Jerison fame) Wrote a calculus text using the idea \(L(x) =\displaystyle\int_0^x {\frac{1}{t}dt} \) as the logarithm. Because Prof Gilliam was also president of then MAA it was a natural for the \(\log(x)\) to become the standard notation and once the computer algebra developers picked it up the old notation was doomed. I had many a fight in directors meetings about that usage (chemistry profs are the worst).
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Standard notation among whom?

And the rest are are subhumans who can be exterminated without regret?
 
JeffM said:
Makes perfect sense, but that is not the whole world.
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Here is an actual story for you. Because we were using a calculus textbook that used that definition for logarithm, the chemistry director raised hel*.
She arranged for one of her faculty who had an undergraduate major in mathematics to teach a course called "calculus for science majors". Well as luck will have it eighteen months later we had a succeeded regional recreational review. Well they would have none of that. The Provost, who himself was a raising star is that group, went through the roof. So any major requiring took the calculus took the course taught by the mathematics department.
 
pka said:
So any major requiring took the calculus took the course taught by the mathematics department.
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When I was at Purdue I started taking Math courses from the Mathematics department. My Physics Professors were a bit aghast and told me that they would teach me all the Math I needed to know. But I have seen time and again that no Physicist can properly teach Math. I asked them what happens when I am facing a problem I've never seen before and they couldn't really answer me.

Though I really would like to know how PhD candidates can learn enough of the Math behind String Theory to be able to reasonably function. (Bonus points there if you caught the pun.) I've been trying to bone up my Math level for 20 years trying to do that.

-Dan
 
pka said:
Here is an actual story for you. Because we were using a calculus textbook that used that definition for logarithm, the chemistry director raised hel*.
She arranged for one of her faculty who had an undergraduate major in mathematics to teach a course in "calculus for science majors". Well as luck will have it eighteen months later we had a succeeded regional recreational review. Well they would have none of that. The Provost, who himself was a raising star is that group, went through the roof. So any major requiring took the calculus took the course taught by the mathematics department.
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I am going to be as non-confrontational as I can, which my colleagues will tell you is not always that non-confrontational. I completely understand why professional mathematicians in a modern context see no need for anything other than the natural log. I get it. It makes sense in the professional and, more importantly, intellectual context of those people.

The immense majority of the world, however, does not consist of professional mathematicians. I guarantee you, from having worked with adolescents, that log to the base 10 is far easier for them to grasp, and the common log makes sense in that context. My son is a computer whatever: those people find log to the base 2 helpful.

My point is that legislating for others is always a claim of absolute authority over others and that no one (except perhaps professional mathematicians) has agreed to accept that professional mathematicians rule the entire world of discourse. I am actually quite sympathetic to the notion that log unadorned should come to mean the natural log because of its centrality in mathematics. The rationale for the utility outside of pedagogy of the common logarithm is gone, and I am not sad: it was ugly mechanics now replaced by the computer and hand calculator. But my experience is that the common logarithm is vital in getting kids to grasp the general concept. And millions of people educated under a different regime of nomenclature should not be dismissed as beneath contempt. Nor am I at all sympathetic to the notion that some self-elected group of academics gets to tell everyone else how to speak.
 
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topsquark said:
When I was at Purdue I started taking Math courses from the Mathematics department. My Physics Professors were a bit aghast and told me that they would teach me all the Math I needed to know. But I have seen time and again that no Physicist can properly teach Math. I asked them what happens when I am facing a problem I've never seen before and they couldn't really answer me.

Though I really would like to know how PhD candidates can learn enough of the Math behind String Theory to be able to reasonably function. (Bonus points there if you caught the pun.) I've been trying to bone up my Math level for 20 years trying to do that.

-Dan
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Well, I was so disgusted with the Math Department at Columbia that I never took a math course there after my freshman year. Horrible, horrible people. It was only when I was in grad school years later that I perceived that I needed to have a better base in math and took more math courses. The result is that I have gaping lacunae in basic math. Of course, in the view of most historians or bankers, I am mathematically erudite, but I am perfectly conscious that that perception is a measure of their ignorance rather than of my knowledge. I believe I understand solidly the little bit of mathematics I know; I know I do not understand any mathematics beyond that.
 
topsquark said:
Okay, but do you have to write it as [math]log_{10}[/math] or something? …
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Oops. When you said math-speak, I thought you were asking for the name.

Yes, for those who use log(x) to mean the natural log, they could write log10(x) to mean the common log. In computer science, I've seen log[10](x), log10(x) and log(10,x) used in systems where log(x) means natural log.

I tutored a student who'd asked the same question you did, but in class. The professor told her, "Like this: logx/log10."

?
 
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