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Math Help - Transposition of logs

  1. #1
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    Transposition of logs

    hi guys/girls

    im struggling with the transposition of the log to eventually find p1. im not sure how to write in this box as a equation so ive added it as a attachment to make it easier to read. i know lp and p2 from my question but need to find the value of p1.

    ive put it as far as i have got but i dont think its right. any help would be great

    Lp=20〖log〗_(10 ) (p2/p1)

    thanks in advance
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  2. #2
    MHF Contributor
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    Re: Transposition of logs

    The inverse function to \log_{10}x is 10^x. So

    Lp=20\log_{10}\left(\frac{p_2}{p_1}\right)

    implies

    10^{-Lp/20}}p_2=p_1.

    Just in case, 10^x=e^{x\ln10} where \ln is logarithm to the base e.
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  3. #3
    MHF Contributor

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    Re: Transposition of logs

    First of all these are \log_{10} not base e.
    So p_1=p_2\cdot 10^{-\frac{Lp}{20}}.
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