47
votes
Should we stop differentiating between ln and log?
Unrelated to US, in Germany the notation through school and university was quite consistent:
$\ln$ using base $e$
$\log$ using base $10$
$\log_x$ using base $x$
I may not know enough about the US ...
- 639
36
votes
Accepted
When writing log, do you indicate the base, even when 10?
And a computer scientist thinks that $\log=\log_2$. I am using $\log$ for the natural logarithm by default in all my courses though I clearly state that in the beginning of each course (I teach at the ...
- 4,439
28
votes
How should I teach logarithms to high school students?
Coming from the perspective of someone who reteaches this material at the college level, neither the graph perspective nor the list of properties perspective really translate into a deep understanding ...
- 5,903
22
votes
Should we stop differentiating between ln and log?
You are wrong about undergraduate courses always treating $\log$ as $\ln$. To my memory, all of my undergrad chemistry and physics (not just general, but majors texts), engineering, calculus, diffyQs, ...
- 237
21
votes
Should we stop differentiating between ln and log?
I would argue that we should never use $\log$ for $\log_{10}$ anymore, only warn that this was historically often done. Sticking to the ISO convention is probably safest:
$$\begin{aligned}
\log_{e} ...
- 692
19
votes
Should we stop differentiating between ln and log?
In mathematics, $\log$ means natural logarithm. So, as you become a mathematician, sometime during that process you must learn this.
That standards document is for natural sciences, not for ...
- 7,637
18
votes
Are there direct practical applications of differentiating natural logarithms?
Have you thought about the fact that you’re asking this in the middle of a pandemic for which log plots are being used all over the place to visualize the growth of COVID cases?
At any rate,
$${d \...
- 5,808
16
votes
Should we stop differentiating between ln and log?
My perspective on this (as a British computer scientist) is slightly different to the others already mentioned: my default expectation is that $\ln$ is the natural logarithm, $\lg$ is the binary ...
- 633
16
votes
How should I teach logarithms to high school students?
How do you teach students about the operator $\sqrt[3]{}$? It's a similar operator in many ways; when dealing with cube roots I try to show them these things:
$\sqrt[3]{x}$ asks "which base to ...
- 21.9k
15
votes
When writing log, do you indicate the base, even when 10?
I'm in Germany (chemist, FWIW). I'm familiar with:
$\log$: base is unknown/not needed (as in $\log (a) + \log (b) = \log (ab)$
natural logarithm: $\ln = \log_e$
base 10 logarithm: $\lg = \log_{10}$
...
- 251
14
votes
Are there direct practical applications of differentiating natural logarithms?
Whenever we measure a quantity on a log scale (such as Richter, decibels, musical pitch, or a log-plot axis), we are focusing attention on relative variation in that quantity. If $y = \ln x$, we have
$...
- 271
14
votes
In teaching mathematics, should one always follow some international standards such as ISO 80000-2?
No.
This standard may be useful for professionals in international settings.
Most teaching happens in smaller, localized settings and things will differ from country to country (e.g. how large ...
- 2,699
12
votes
In teaching mathematics, should one always follow some international standards such as ISO 80000-2?
The standard that you link to (ISO 80000-2:2009) seems to be not available for free. That is, in order for me to follow the standard, I have to be able to read it, and in order for me to read it, I ...
- 10.9k
11
votes
Does anyone teach logarithms via slide rules?
A few thoughts:
Joe Pasquale from UCSD has done similar things:
https://cseweb.ucsd.edu/~pasquale/SlideRuleTalkLasVegas14.pdf and
https://cseweb.ucsd.edu/~pasquale/FreshmanSeminarF03/
If the ...
- 111
11
votes
Applications for logarithms in a business math course
I feel compelled to provide your "of course" answer of exponential growth/decay. This answer is hopefully appropriate for lower-level business courses such as high-school level.
Here's a ...
- 241
11
votes
Antiderivative of $1/x$, with or without absolute value?
Even $\int \frac{1}{x} \textrm{ d}x = \ln(|x|) + C$ is incorrect.
It should be
$$
\int \frac{1}{x} \textrm{ d}x = \begin{cases}
\ln(x) + C_1 \textrm{ if $x > 0$}\\
\ln(-x) + C_2 \textrm{ if $x < ...
- 25.8k
9
votes
Does anyone teach logarithms via slide rules?
but I wonder if those who have, ever bring in to the classroom slide rules as "props"?
In the Olden Days (before hand-held calculators) I remember that we had (at Ohio State) a big demonstration ...
- 7,637
9
votes
Logarithms properties, continuity and circular reasoning
In my opinion, one should forget about trying to be rigorous when introducing logarithms to high school students, or anyone who hasn't seen logarithms before. For students like this, I agree with the ...
- 1,332
8
votes
Should we stop differentiating between ln and log?
This question is more difficult to answer than it appears. Part of the difficulty is that usage varies from area to area, from country to country, and from teacher to teacher. Part of the problem is ...
- 5,879
8
votes
Sliderule for teaching logarithms
As Daniel's answer states, the most likely reason why slide rules are rarely used to teach logarithms boils down to them being hard to come by. As they have been replaced by electronic calculators, it ...
- 921
8
votes
In teaching mathematics, should one always follow some international standards such as ISO 80000-2?
Another point. It seems to me that someone who's trained to think that there's only one way to write everything might well be trained to think less in general. If you know that $\mathbb N$ may or may ...
- 571
8
votes
Does anyone teach logarithms via slide rules?
(too-long comment) I think it's a nice adjunct, but I would not introduce the topic that way. Introduce it after teaching of rational (math meaning) exponents and roots in a rational (well thought ...
- 325
7
votes
How should I teach logarithms to high school students?
I would start with explaining exponentials as repeated multiplication. For example, we look at the sequence $2^1=2$, $2^2=2\times 2$, $2^3=2\times 2\times 2$... and call it one 'two', two 'twos', ...
6
votes
Are there direct practical applications of differentiating natural logarithms?
I couldn't find a lot either. Suggest playing with some logarithmic properties and constructing problems based on that.
E.g. pH is log10 of the hydronium ion concentration. Could ask how the pH ...
- 159
6
votes
Accepted
Does anyone teach logarithms via slide rules?
I have my college algebra students create slide rules each semester.
Key pedagogical question:
What is the point of having an algebra student construct a slide rule?
Possible answers:
The goal is ...
- 21.9k
6
votes
Accepted
Define logarithmic function by functional relation
Find all applications $f$ from $\mathbb{R} \to \mathbb{R}$
such that (1) is satisfied, posing all the necessary restrictions.
From the textbook Calculus 9th edition by Salas, Hille, Etgen (section 7....
- 76
5
votes
Are there direct practical applications of differentiating natural logarithms?
Boltzmann's equation for entropy is $S=k\ln W$, and the second law of thermodynamics is all about change in entropy. Maybe this is a place to start with your quest for a practical application of the ...
- 11.1k
5
votes
How should I teach logarithms to high school students?
Instant intuition giver: Logarithm computes the number of digits.
One could start by letting the students think how such a function should behave.
One possible idea: That's just for whole numbers. Is ...
- 159
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