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Math Help - Need help with the setting up the intial equation

  1. #1
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    Need help with the setting up the intial equation

    Richter Scale equation: logE= 4.4 + 1.5M

    Suppose that the magnitudes of two earthquakes differ by 1 on the Richter Scale. Find the ratio of the released energy of the larger earthquake to that of the smaller earthquake.
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by vinson24 View Post
    Richter Scale equation: logE= 4.4 + 1.5M

    Suppose that the magnitudes of two earthquakes differ by 1 on the Richter Scale. Find the ratio of the released energy of the larger earthquake to that of the smaller earthquake.

    if I understand the question

    first magnitude energy let it be

    \log E_1 = 4.4 1.5M

    natural log have the base 10 \log_{10} E_1 = 4.4 + 1.5M

    so E_1 = 10^{4.4 + 1.5M}

    second magnitude

    \log_{10} E_2 = 4.4 + 1.5(M+1)

     E_2 = 10^{4.4 + 1.5(M+1)}

    \frac{E_2}{E_1} = \frac{10^{4.4 + 1.5M + 1.5}}{10^{4.4+1.5M}}

    \frac{E_2}{E_1} = \frac{10^{4.4}\cdot 10^{1.5M}\cdot 10^{1.5}}{10^{4.4}\cdot 10^{1.5M}} = 10^{1.5}
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