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Math Help - Rewriting expression as single log with coefficent 1

  1. #1
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    Rewriting expression as single log with coefficent 1

    I am rewriting the following as a single log with a coefficient of 1:

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

    Because the coefficient is already zero, I believe I need to divide the two expressions:

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

    And cancel out the ones...

    ln ( (x^3) / ((x^2) + x) )

    This seems too easy - can I break it down further?
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  2. #2
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    Quote Originally Posted by Snowcrash View Post
    I am rewriting the following as a single log with a coefficient of 1:

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

    Because the coefficient is already zero, I believe I need to divide the two expressions:

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

    And cancel out the ones...

    ln ( (x^3) / ((x^2) + x) )
    You know that cannot be done.
    Only factors can be divided out.
    But this is true (x^3-1)=(x-1)(x^2+x+1)

    So this is also true \ln \left( {\frac{{x^3  - 1}}{{x^2  + x + 1}}} \right) = \ln \left( {x - 1} \right). WHY?
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  3. #3
    MHF Contributor red_dog's Avatar
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    \ln\frac{x^3-1}{x^2+x+1}=\ln\frac{(x-1)(x^2+x+1)}{x^2+x+1}=\ln(x-1)
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