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Math Help - Combining into single logarithm?

  1. #1
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    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.
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  2. #2
    MHF Contributor Siron's Avatar
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    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)
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  3. #3
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    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?
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  4. #4
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    Re: Combining into single logarithm?

    Quote Originally Posted by FatimaA View Post
    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)
    Thanks from FatimaA
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