# Thread: Combining into single logarithm?

1. ## Combining into single logarithm?

Need some help with this. Not understanding my notes on the lecture.

Simplify the following by combining all terms into a single logarithm.

ln(x^2)+(1/3)ln(x-2)-4

Thanks to anyone who helps.

2. ## Re: Combining into single logarithm?

You have to use:
$\log(ab)=\log(a)+\log(b)$
$\log\left(\frac{a}{b}\right)=\log(a)-\log(b)$
$\log(a^b)=b\log(a)$

3. ## Re: Combining into single logarithm?

Yeah I know what the properties are but I don't know how to apply them to this particular problem.

This was what I got and I have no idea if it's right:

1) ln(x^2)+(1/3)ln(x-2)-4
2) = ln(x^2)+ln((x-2)-4)^1/3
3) = ln(x^2((x-2)-4)^1/3

Would you someone mind checking this and showing me how to do it right?

4. ## Re: Combining into single logarithm?

Originally Posted by FatimaA
Simplify the following by combining all terms into a single logarithm.

ln(x^2)+(1/3)ln(x-2)-4
$\ln(x^2) + \ln{\sqrt[3]{x-2}} - \ln(e^4)$

$\ln\left(\frac{x^2 \sqrt[3]{x-2}}{e^4}\right)$