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Math Help - Finding the magnitude with Logs.

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    Finding the magnitude with Logs.

    I've been stuck on this problem for a long time now. Can someone help me? Thanks in advance


    The magnitude of an earthquake is measured relative to the strength of a “standard” earthquake, whose seismic waves are of size W0. The magnitude, M, of an earthquake with seismic waves of size W is defined to be
    .The value of M is called the Richter scale rating of the strength of an earthquake.

    How many times larger are the seismic waves of the earthquake with rating of 5.7 on the Richter scale, than the seismic waves of the earthquake with a rating of 3.6 to the nearest integer.
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    Quote Originally Posted by JC05 View Post
    I've been stuck on this problem for a long time now. Can someone help me? Thanks in advance


    The magnitude of an earthquake is measured relative to the strength of a “standard” earthquake, whose seismic waves are of size W0. The magnitude, M, of an earthquake with seismic waves of size W is defined to be
    .The value of M is called the Richter scale rating of the strength of an earthquake.

    How many times larger are the seismic waves of the earthquake with rating of 5.7 on the Richter scale, than the seismic waves of the earthquake with a rating of 3.6 to the nearest integer.
    let the intensity of the 5.7 quake = W_1 , intensity of the 3.6 quake = W_2

    5.7 = \log\left(\dfrac{W_1}{W_0}\right)

    3.6 = \log\left(\dfrac{W_2}{W_0}\right)

    take the difference between the two equations ...

    2.1 = \log\left(\dfrac{W_1}{W_0}\right) - \log\left(\dfrac{W_2}{W_0}\right)

    use the difference property of logarithms ...

    2.1 = \log\left(\dfrac{W_1}{W_2}\right)

    change to an exponential equation ...

    \dfrac{W_1}{W_2} = 10^{2.1} \approx 126 times greater
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