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Math Help - expanding log

  1. #1
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    expanding log

    i need help expanding this expression as in rewrite it with multiple logs

    ln 5√(4x-1/4x+1)

    the 5
    √ is a 5th root.
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  2. #2
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    Quote Originally Posted by burner View Post
    i need help expanding this expression as in rewrite it with multiple logs

    ln 5√(4x-1/4x+1)

    the 5
    √ is a 5th root.
    \ln\left[\frac{(2x-1)(2x+1)}{4x^2+1}\right]^{\frac{1}{5}}

    now use these three log properties ...

    \log{a^c} = c\log{a}

    \log\left(\frac{a}{b}\right) = \log{a} - \log{b}

    \log(ab) = \log{a} + \log{b}
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  3. #3
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    Quote Originally Posted by burner View Post
    i need help expanding this expression as in rewrite it with multiple logs

    ln 5√(4x-1/4x+1)

    the 5
    √ is a 5th root.
    1. Re-write the given term:

    \sqrt[5]{\dfrac{4x^2-1}{4x^2+1}} = \left((2x-1)(2x+1)(4x^2+1)^{-1}  \right)^{\frac15}

    And now use logarithm:

    \log\left(\sqrt[5]{\dfrac{4x^2-1}{4x^2+1}}  \right) = \dfrac15 \left(\log(2x-1) + \log(2x+1) - \log(4x^2+1)\right)


    EDIT Beaten again ...
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  4. #4
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    ty for ur help i get it now
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