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Math Help - Expanding an expression

  1. #1
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    Expanding an expression

    Can anyone help with this?



    Thanks in advance!
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  2. #2
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    Quote Originally Posted by dmfan2009 View Post
    Can anyone help with this?



    Thanks in advance!
    \ln\left(\sqrt{x^4\sqrt{y^4\sqrt{z^2}}}\right)

    \frac{1}{2}\ln\left(x^4\sqrt{y^4\sqrt{z^2}}\right)

    \frac{1}{2}\ln(x^4) + \ln\left(\sqrt{y^4\sqrt{z^2}}\right)

    \frac{1}{2}\ln(x^4) + \frac{1}{2}\ln\left(y^4\sqrt{z^2}\right)

    keep going ...
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  3. #3
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    Remember, your properties of log says that \log_{a}(MN)=\log_{a} M + \log_a{N}.

    To start, I would make your roots exponents. It would be ln (x^\frac{4}{2} y^\frac{4}{4}z^\frac{2}{8}).

    So using that first property, we would have ln \ x^\frac{4}{2} + ln\ y^\frac {4}{4} + ln\ z^\frac{2}{8}.

    Another property of logs says that \log_{a}M^r = r\ log_{a}M

    So we could bring your exponents in front and it would look like
    \frac {4}{2} ln \ x + \frac {4}{4} ln \ y + \frac{2}{8} ln \ z

    You could essentially reduce your fractions, but it is easier to put back together into your original problem with the fractions not reduced.
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