Combining into single logarithm?

Apr 2012
72
0
Seattle, Washington
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.
 
Jul 2011
1,254
389
Belgium
You have to use:
\(\displaystyle \log(ab)=\log(a)+\log(b)\)
\(\displaystyle \log\left(\frac{a}{b}\right)=\log(a)-\log(b)\)
\(\displaystyle \log(a^b)=b\log(a)\)
 
Apr 2012
72
0
Seattle, Washington
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?
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
Simplify the following by combining all terms into a single logarithm.

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

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