# Tag Info

### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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: $\lg = \log_{10}$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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', ...

### 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 ...
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### 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 ...
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### 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....
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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 ...