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Questions tagged [logarithm]

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2 votes
3 answers

Logarithms properties, continuity and circular reasoning

I have a doubt relating to logarithms. Anticipating some answers, I know that a "mathy" way of doing things is defining the function by its properties ($f(xy)=f(x)+f(y)$) and then just build ...
Curious student's user avatar
2 votes
1 answer

Define logarithmic function by functional relation [closed]

My son was working the other day with exercises such as: Find all the mappings $f:\mathbb{N}\rightarrow\mathbb{Z}$ verifying $$\forall m,n \in \mathbb{N}, f(m+n)=f(n)+f(m).$$ As another example: Find ...
Dimitris's user avatar
  • 165
5 votes
4 answers

Antiderivative of $1/x$, with or without absolute value?

Many textbooks include $\int \frac{1}{x} dx = \ln |x| + c$ in their list of antiderivative formulas, with the absolute value. Correspondingly, they do the same with the antiderivative of $\tan x$ or ...
Hnrt's user avatar
  • 51
14 votes
5 answers

When writing log, do you indicate the base, even when 10?

I’ve been working with many students on logarithms and have noted that log has a base of 10 unless specified. Further, I commented that putting a 10 as a subscript to log is redundant, or at least not ...
JTP - Apologise to Monica's user avatar
14 votes
7 answers

Applications for logarithms in a business math course

Context: I am an assistant professor at a small liberal arts institution in the US. The title really says it all: I am looking to provide applications for logarithms in a business math course (most ...
AegisCruiser's user avatar
  • 1,427
19 votes
10 answers

How should I teach logarithms to high school students?

I have some very basic questions about how to teach the logarithm to high school students: First of all, is it better to introduce it as a function with a graph or is it better to treat it like a ...
Matt N.'s user avatar
  • 317
2 votes
3 answers

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 ...
Michael Hardy's user avatar
16 votes
6 answers

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 ...
Amos Hunt's user avatar
  • 361
20 votes
4 answers

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 ...
Joseph O'Rourke's user avatar
27 votes
6 answers

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 ...
Nahmid's user avatar
  • 403
8 votes
5 answers

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 ...
Zuriel's user avatar
  • 4,275
2 votes
0 answers

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)+...
reuns's user avatar
  • 129
11 votes
1 answer

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 ( and have been surprised to find very little reference to exponential functions and logarithms. ...
mweiss's user avatar
  • 17.4k
7 votes
3 answers

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) +...
nosyarg's user avatar
  • 295
17 votes
4 answers

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 ...
Joonas Ilmavirta's user avatar
12 votes
8 answers

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,...
Joseph O'Rourke's user avatar
14 votes
1 answer

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 ...
Karl's user avatar
  • 1,552
13 votes
2 answers

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 ...
Jhecht's user avatar
  • 263
8 votes
9 answers

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 ...
JTP - Apologise to Monica's user avatar