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Math Help - solving this log

  1. #1
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    solving this log



    Please can someone take me through it
    Much appreciated
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  2. #2
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    Quote Originally Posted by 200001 View Post


    Please can someone take me through it
    Much appreciated
    You should use the following properties of the log-function:

    \log(a) + \log(b) = \log(ab)

    \log(a) - \log(b) = \log \left(\frac ab \right)

    n \cdot \log(a)  = \log(a^n)

    \frac1n \cdot \log(a)=\log \left(\sqrt[n]{a} \right)
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  3. #3
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    Hi
    thanks
    Im ok with the laws of logs but cant seem to get this one going for some reason
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  4. #4
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    Quote Originally Posted by 200001 View Post


    Please can someone take me through it
    Much appreciated
    \frac{1}{4}\,log_5 \left(\frac{5}{3}\right) + \frac{1}{3}log_5 \left(2 \cdot 7\right)
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  5. #5
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    Quote Originally Posted by 200001 View Post
    Hi
    thanks
    Im ok with the laws of logs but cant seem to get this one going for some reason
    {\color{blue}\frac14 \cdot \left(\log_5(5) - \log_5(3)  \right) } + \frac13 \cdot \left(\log_5(2) + \log_5(7)  \right)

    {\color{blue}\log_5 \left(\sqrt[4]{ \frac53  }  \right) }+ \frac13 \cdot \left(\log_5(2) + \log_5(7)  \right)

    I've transformed the first summand according the laws of logarithms. I'll leave the second summand for you. Afterwards combine both summands to get one term.
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