# Can you distribute logarithms?

1. Aug 11, 2013

### mileena

Does anyone know if the following is true:

logb (x + y) = logb x + logb y

Thanks. This isn't homework, but I am just wondering if the following is true. I already know the logarithm product, quotient, and power rules!

Last edited: Aug 11, 2013
2. Aug 11, 2013

### micromass

Why don't you try to find a counterexample?

3. Aug 11, 2013

### mileena

Ok, good idea. I don't know how to use a scientific calculator yet to figure out logs, but I know they are online. I will plug in some real numbers to see if the equation s true or not.

4. Aug 11, 2013

### mileena

Ok, I just did, using log 2 and log 3, and then again with log 8 and log 10. It worked! you can distribute logs!

Thanks, and sorry for posting so many questions in one day.

5. Aug 11, 2013

### micromass

It shouldn't work

Can you post what you did?

6. Aug 11, 2013

### junaid314159

7. Aug 11, 2013

### johnqwertyful

log(2)=log(1+1)=log(1)+log(1)

Is this true?

8. Aug 11, 2013

### Staff: Mentor

What's the log of 1?
What's the log of 2?

9. Aug 11, 2013

### micromass

I think he knows lol. He just asked it to the OP :tongue:

10. Aug 11, 2013

### Staff: Mentor

Oops - right you are. Sorry about that.

11. Aug 11, 2013

### symbolipoint

Make and test an example. Imagine your base is 10, and x=100 and y=10,000,000.

log10(100+10000000)=log10(100)+log10(10000000)
Does this make sense? Does this not make sense?

12. Aug 12, 2013

### mathman

Log(xy) = log(x) + log(y). Unless xy = x+y, your equation is wrong.

13. Aug 12, 2013

### mileena

Hi, sorry for not posting sooner, but I was busy all day and I don't really have Internet access until I get to the library.

Let me also say that I am an idiot!

Yesterday, I said that you could distribute logs, so that:

logb (x + y) = logb (x) + logb (y)

But I made a mistake. Instead of adding, for example, 2 and 3, and taking the log of 5 and comparing that with the sum of log 2 and log 3, I multiplied 2 and 3! Thus I got:

logb x + logb y = logb (xy)

which is, of course, the product rule.

14. Aug 12, 2013

### symbolipoint

I did not say that the equation was correct. I only presented it, and then asked two questions. I know already that the equation is wrong. mileena already found understanding that was sought.

15. Aug 12, 2013

### junaid314159

@symbolipoint: I think mathman may have been responding to the original post when he was commenting.

@Nugatory: log 1 = 0 and log 2 ≈ 0.6931...

-Junaid :tongue:

16. Aug 13, 2013

### symbolipoint

mathman, that is possible. I inferred that you may have responded to my post because yours came directly after it, and other interrelations of responses of posts were not clear.

I tried to give an example to be checked and asked if the example made sense.

17. Aug 13, 2013

### mathman

I was responding to the original post.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook