Questions tagged [logarithm]
The logarithm tag has no usage guidance.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
- 1,690
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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 ...
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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 ...
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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 ...
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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 ...
- 4,245
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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)+...
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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. ...
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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) +...
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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 ...
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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,...
- 29.5k
14
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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 ...
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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 ...
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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 ...