Logarithmic Expressions Simplified

[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...

 

[symbolipoint]

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

The rest of the stuff you wrote is unintelligible.

 

[HallsofIvy]

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

That would be log((a/10b)

 

[ehild]

That would be log((a/10b)

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

ehild

 

[HallsofIvy]

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).

 

[ehild]

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).

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

ehild

 

[lionely]

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

 

[Mark44]

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

Not only that, but your first post is extremely unclear as to what you're trying to do.

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...

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))

 

[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)?

 

[Mark44]

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

for this part I'm kind of confused if it's log(a/b)/10

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.

shouldn't you invert and multiply and get log(10a/b)?

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

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

 

[Mark44]

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.

 

[lionely]

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

 

[Mark44]

Seems like a good idea to me.