Logarithmic Expressions Simplified

  • Thread starter lionely
  • Start date
  • Tags
    Log
In summary, the conversation discusses an expression involving logarithms and the confusion surrounding its simplification. The final simplified expression is log(a/(10b)). There is also a mention of a potential error in the back of the book, where the answer is given as 10b/a instead.
  • #1
lionely
576
2
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...
 
Physics news on Phys.org
  • #2
This is an expression: log(ab)-2logb -1
What do you want from it?

The rest of the stuff you wrote is unintelligible.
 
  • #3
He stated that in the title, not in the body: express as a single iogarithm.

That would be log((a/10b)
 
  • #4
HallsofIvy said:
That would be log((a/10b)

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

ehild
 
  • #5
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
HallsofIvy said:
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)) :tongue2:

ehild
 
  • #7
Oh.. my order of operation was wrong.. thanks.
 
  • #8
lionely said:
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.
lionely said:
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))
 
  • #9
= 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
lionely said:
= 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.

lionely said:
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.

$$ \frac{a/b}{10} = \frac{a}{b} \cdot \frac{1}{10} = \frac{a}{10b}$$
 
  • #11
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
oh... I guess I need to do some work on basic algebra...
 
  • #13
Seems like a good idea to me.
 

What does it mean to "express this as one log"?

Expressing an equation or expression as one log means to rewrite it in a simplified form using only a single logarithm.

Why is it important to express an equation as one log?

Expressing an equation as one log can make it easier to solve and can also help to identify patterns and relationships between variables.

How do you express an equation as one log?

To express an equation as one log, you can use the properties of logarithms, such as the product, quotient, and power rules, to combine multiple logarithms into a single one.

What are the common properties of logarithms used in expressing an equation as one log?

The common properties of logarithms used in expressing an equation as one log include the product rule, quotient rule, power rule, and the change of base formula.

Can an equation always be expressed as one log?

No, not all equations can be expressed as one log. Some equations may require multiple logarithms or cannot be simplified using the properties of logarithms.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
8
Views
633
  • Precalculus Mathematics Homework Help
Replies
18
Views
984
  • Precalculus Mathematics Homework Help
Replies
7
Views
763
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
848
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
3
Views
413
Back
Top