# Questions tagged [logarithm]

The tag has no usage guidance.

19 questions
Filter by
Sorted by
Tagged with
419 views

### 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 ...
191 views

### 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 ...
• 165
380 views

### 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 ...
• 51
3k views

### 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 ...
3k views

### 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 ...
• 1,427
7k views

### 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 ...
• 317
344 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 ...
• 1,883
3k 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 ...
• 361
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 ...
• 29.8k
11k 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 ...
• 403
2k 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 ...
• 4,275
121 views

• 295
829 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 ...
• 3,760
846 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,...
• 29.8k
189 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 ...
• 1,552
### 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 ...