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Math Help - ln division question (precalc section?)

  1. #1
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    Exclamation ln division question

    I have the problem
    Expand:

    4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)

    Is it legal to distribute ln like this?

    Here is what I got:

    4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)

    Thanks.
    Last edited by CaptainBlack; May 26th 2010 at 06:28 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by dwatkins741 View Post
    I have the problem
    Expand:

    4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)

    Is it legal to distribute ln like this?

    Here is what I got:

    4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)

    Thanks.
    No, you can see that by applying the laws of logarithms to

    \left(\frac{2\ln(x)+\ln(3)}{2}\right)=\left( \frac{\ln(3x^2)}{2}\right) \ne \left(\frac{\ln(x^2+3)}{2}\right)

    CB
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  3. #3
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    Quote Originally Posted by dwatkins741 View Post
    I have the problem
    Expand:

    4\ln(x)+\left(\frac{\ln(x^2+3)}{2}\right)

    Is it legal to distribute ln like this?

    Here is what I got:

    4\ln(x)+\left(\frac{2\ln(x)+\ln(3)}{2}\right)

    Thanks.
    Dear dwatkins,

    \ln{(a\times{b})}=\ln{(a)}+\ln{(b)}~but~\ln(a+b)\n  eq{\ln{(a)}+\ln{(b)}}

    You could find more information about identities of logarithms at, List of logarithmic identities - Wikipedia, the free encyclopedia

    Hope this will help you.
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