# Any ideas why this law of logs problem is marked incorrect?

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1. Dec 12, 2014

### Niaboc67

Thanks

2. Dec 12, 2014

### ehild

It is correct, but you can expand x2-25 further. And note that |x|>5

3. Dec 12, 2014

### Niaboc67

so instead of 25 it would be 5?

4. Dec 13, 2014

### Staff: Mentor

What ehild means in the last sentence is that you must have |x| > 5.

No, what he's saying is that you can factor x2 - 25.

5. Dec 13, 2014

### ehild

I also meant that the expression is not defined for |x| ≤ 5. You have to exclude it. And when expanding x2-25, log(x-5) is only defined if x>5,

6. Dec 13, 2014

### Fredrik

Staff Emeritus
The original expression is defined for all $x$ such that $|x|>5$. (These values of $x$ make the thing under the square root positive). But $\log(x-5)$ is defined for all $x$ such that $x>5$. So $\log(x-5)$ isn't defined for all $x$ such that the original expression makes sense. This seems like a good reason to not do the rewrite $\log(x^2-25)=\log(x+5)+\log(x-5)$.

7. Dec 13, 2014

### ehild

Yes, the expression can not be really expanded further for all x. Why was it marked incorrect then?

8. Dec 13, 2014

### BruceW

I'm guessing it is an online system which the answer is typed into, and automatically marked... So maybe it is because the 5 was placed right before the log, as in
5log, and maybe the computer did not recognize this as 5*log ?

9. Dec 13, 2014

### Niaboc67

I understand now. The x-25 could have been factored more. Thanks guys!

10. Dec 13, 2014

### Staff: Mentor

Just to be clear, that should be x2 - 25.

11. Dec 13, 2014

### Fredrik

Staff Emeritus
The $x^2-25$ can be factored, but we also said that it shouldn't be, because you don't want a final answer that makes sense for a smaller set of values of $x$ than the original expression. For example, the original expression makes sense when $x=-7$, but an expression that contains $\log(x-5)$ doesn't. So we don't know why the answer you posted was marked incorrect. See BruceW's post for a possible reason.