Expressing this as one log

1. Nov 14, 2012

lionely

Everything is base 10

log(ab)-2logb -1

a+b/ b2 = a/b/10 = 10a/b?

But in the back of the book the answer is 10b/a...

2. Nov 14, 2012

symbolipoint

This is an expression: log(ab)-2logb -1
What do you want from it?

The rest of the stuff you wrote is unintelligible.

3. Nov 14, 2012

HallsofIvy

Staff Emeritus
He stated that in the title, not in the body: express as a single iogarithm.

That would be log((a/10b)

4. Nov 14, 2012

ehild

Are you sure? :tongue: One parenthesis missing, is b in the numerator or in the denominator?

ehild

5. Nov 14, 2012

HallsofIvy

Staff Emeritus
Oh, dear, an extra parenthesis! It should be log(a/10b). The "b" is in the denominator. Prior to canceling, log(ab)- 2log(b)- 1= log(ab)- log(b^2)- log(10)= log(ab/10b2).

6. Nov 14, 2012

ehild

A missing parenthesis: log(ab)-log(b2)-log(10)=log(ab/(10b2))=log(a/(10b)) :tongue2:

ehild

7. Nov 14, 2012

lionely

Oh.. my order of operation was wrong.. thanks.

8. Nov 14, 2012

Staff: Mentor

Not only that, but your first post is extremely unclear as to what you're trying to do.
1. Connect expressions that have the same value with =.
2. Keep track of what you're doing. In the first line above, you have two log expressions. In the second line, you show no indication that you're working with logs.
3. Indicate exponents so that we can tell what you mean. At the very least, use ^ to indicate an exponent, as in b^2. Even better would be to use the Advanced Menu (click Go Advanced, and use the X2 button, which adds HTML tags for exponents.)

log(ab)-2logb -1
= log(ab) - log(b2) - log(10)
= log(ab/b2) - log(10)
= log(a/b) - log(10)
= log(a/(10b))

9. Nov 14, 2012

lionely

= log(a/b) - log(10)
= log(a/(10b))

for this part I'm kind of confused if it's log(a/b)/10 shouldn't you invert and multiply and get log(10a/b)?

10. Nov 14, 2012

Staff: Mentor

That's not what I wrote. What you have here is
$$\frac{log(a/b)}{10}$$

What I wrote is
$$log(\frac{a/b}{10})$$

I hope that you can see that these are different.

Your confusion here seems to be with basic arithmetic, particularly how fraction division works.

$$\frac{a/b}{10} = \frac{a}{b} \cdot \frac{1}{10} = \frac{a}{10b}$$

11. Nov 14, 2012

Staff: Mentor

If, as you say, the book gives the answer as 10b/a, then either you haven't written the problem correctly or the book's answer is wrong.

12. Nov 15, 2012

lionely

oh... I guess I need to do some work on basic algebra......

13. Nov 15, 2012

Staff: Mentor

Seems like a good idea to me.