Questions tagged [logarithm]

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2
votes
2answers
217 views

Logarithms chronologically before algebra

Do any textbooks or (somewhat?) standard curricula introduce logarithms and their applications in arithmetic without assuming the students know any algebra? (I do not mean just the use of logarithms ...
16
votes
6answers
2k views

Are there direct practical applications of differentiating natural logarithms?

The textbook I am using to teach Calculus I includes in the exercises of most chapters a number of interesting real-world applications of the concepts from that chapter. However, the chapter on the ...
16
votes
4answers
3k views

Does anyone teach logarithms via slide rules?

I just inherited two slide rules from my grandfather-in-law, one wood with smooth action despite nearly a century without use.1 (I used a K+E slide rule myself as an undergraduate in the 1970's.) It ...
26
votes
6answers
10k views

Should we stop differentiating between ln and log?

In many U.S. middle schools and high schools, $\ln$ and $\log$ are treated differently, with the intent that $\log$ is equivalent to $\log_{10}$. However, in undergraduate courses and in the academic ...
7
votes
4answers
460 views

In teaching mathematics, should one always follow some international standards such as ISO 80000-2?

ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO). In teaching mathematics, should one always follow this ...
2
votes
0answers
110 views

Complex logarithm and $\mathbb{C}/2i\pi \mathbb{Z}$

Is it possible and is it a good idea to introduce the additive group and metric space $\mathbb{C}/2i\pi \mathbb{Z}$ very soon, at the same time as the complex logarithm $\log(r e^{i \theta}) = \ln(r)+...
11
votes
1answer
530 views

What do the Common Core Standards expect secondary students to learn about logarithms or the number $e$?

I've been looking through the Common Core State Standards (http://www.corestandards.org/Math/) and have been surprised to find very little reference to exponential functions and logarithms. ...
7
votes
3answers
622 views

Sliderule for teaching logarithms

I recently learned how to use a slide rule and I have since been wondering why they are not commonly used to teach properties of logarithms. It seems that they are very clear examples of the $\log(a) +...
16
votes
4answers
607 views

Do students confuse $\log_ab$ and $\log a^b$?

I recently observed a group of students being introduced to logarithms for the first time. Some of them had trouble writing $\log_ab$ properly, and it looked more like $\log a^b$. All logarithms have ...
11
votes
8answers
545 views

How best to explain the logarithm to the mathematically naive?

Suppose you need to explain "What is a logarithm?" to an intelligent but math-phobic adult (or a student well-prior to her introduction to logarithms).1 I have used base-$10$, saying that, essentially,...
14
votes
1answer
158 views

Resources suitable for a beginners' course with exponentials

I'm currently involved in developing materials for a new UK tier of examination known as Core Maths. The course is designed for 16-18 year olds to further their mathematics education but without ...
11
votes
2answers
1k views

Logarithm Tables - How were the values reached?

I'm teaching an Algebra II/Trigonometry class that is currently working on logarithms as the inverse function of exponential functions. Now, to keep their interest I had them struggle for a few ...
8
votes
7answers
873 views

Method of Solving $5^x=326$ (Logs not allowed)

$5^x=326$ A book titled "algebra and trigonometry" by Paul Foerster, offers this problem. It came before the logarithm chapter and specifically said not to solve with any log manipulation. It ended ...