# Intro Math Are there any good math books with logarithm basics?

1. Jul 15, 2017

### awholenumber

I have a couple of college algebra textbooks , but none has some proper intro to logarithm basics .
I like to keep a book for logarithm alone , i see some online PDF's on logarithm , but all are sort of messed up .

2. Jul 15, 2017

### vanhees71

Well, you define the natural logarithm as the inverse of the exponential function, which itself is completely defined on entire $\mathbb{C}$ by its power series. Why one should need an extra textbook for this pretty unproblematic subject is not clear to me. You find it in any Analysis I book (for real numbers at least).

3. Jul 15, 2017

### awholenumber

4. Jul 15, 2017

### MidgetDwarf

You need to know Calculus if you want to understand why the exponential functions, and it's inverse behaves.

You have to take definitions as is, for now.

5. Jul 15, 2017

### MidgetDwarf

The main idea for the log. Is you need to show what it means for a function to have an inverse.

Then you need to know about limits... etc

The MVT is used for the proof of this.

Pretty

6. Jul 16, 2017

### mathwonk

i recommend eulers algebra book, available free online

7. Jul 16, 2017

### awholenumber

Thanks a lot for all the replies :-)

8. Jul 17, 2017

### Staff: Mentor

I disagree. Most algebra books at the precalculus level present exponential functions and their graphs, and there isn't anything very deep about the graphs of, say, y = 2x or y = 10x. Each of these exponential functions has a log function defined as its inverse, as e.g.,
$y = 10 ^x \Leftrightarrow x = log_{10}(y)$

The concept of the inverse of a function doesn't require calculus or limits.

9. Jul 17, 2017

### Staff: Mentor

Any decent college algebra textbook should have a "proper" introduction to the basics of logarithms. It doesn't require a whole book to cover this relatively small topic.

10. Jul 18, 2017

### symbolipoint

That's about right. You learn the "basics" of logarithms when you study Intermediate Algebra, and you go through the same in your College Algebra course (including their textbooks). You review exponential functions in Intermediate Algebra, learn about inverse functions, and then are instructed how the logairthm is the inverse of exponential function.

11. Jul 18, 2017

### MidgetDwarf

The proof of inverse of exponentials does...

12. Jul 18, 2017

### Buffu

I think you need higher algebra by Hall and Knight.

13. Jul 18, 2017

### Staff: Mentor

Not if you define logarithms as the inverses of exponential functions. Since the OP asked specifically about logarithm basics, it really isn't necessary to define $\ln(x)$ in terms of an integral.
If you don't mind a book that was written in 1887. It's certainly comprehensive in what it covers, and would serve as an excellent reference of what used to be taught in algebra classes over a century ago. The book would not be useful for a student who plans to take calculus, as it doesn't consider functions and their graphs -- in fact, there's not a single image in the entire book.

14. Jul 18, 2017

### Buffu

Why you need graphs ?

15. Jul 18, 2017

### Staff: Mentor

You're kidding, right? There's an old saying, "A picture is worth a thousand words."

A graph conveys a lot of important information that can be grasped almost instantly, such as its intercepts, where it is increasing or decreasing, its concavity, and more.

16. Jul 18, 2017

### awholenumber

17. Jul 26, 2017