LN equation help

1. Jul 17, 2008

babacanoosh

1. lnx + ln(x+2) = ln3

2. just work the problem out using distributive property

3.
ln2x = ln3-ln2
ln2x = .4054/b]

ehh..I am just doing this one wrong. It is hard to believe what summer vacation can do to you

2. Jul 17, 2008

rocomath

$$\ln ab=\ln a+\ln b$$

Use that property on the left side then use the fact that "e" is the inverse of natural log.

3. Jul 17, 2008

babacanoosh

ok great i got it. Thanks a lot. But for some reason my answers are 3 and negative 1. Now i know that that would mean that the answer would only be 3 but the right answer is 1. Instead of getting a -1, 3...the right answer is -3, 1.

I tried what you described, in the end getting x^2 +2x -3

Thanks

4. Jul 17, 2008

rocomath

$$\ln{x(x+2)}=\ln 3$$

$$x^2+2x-3=0$$

$$(x-1)(x+3)=0$$

So can you have the negative 3?

5. Jul 17, 2008

babacanoosh

no you cannot. Thank you

6. Jul 17, 2008

rocomath

Sure?

The Domain of $$\ln x$$ is $$x > 0$$

Similarly, $$x(x+2)>0$$

What values satisfy this inequality?

7. Jul 17, 2008

babacanoosh

oh! I see. When plugging in -3, it does work.

8. Jul 17, 2008

rock.freak667

Wait...For lnx + ln(x+2) = ln3, if you put in x=-3 it doesn't work.

But it works for lnx(x+2)=ln3. How do you know whether it is valid or not?

9. Jul 18, 2008

arildno

Correct.

Indeed it does.
Remember that the argument to the logarithms can't be non-positive.

Your ORIGINAL equation cannot therefore have non-positive solutions.