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March 30, 2017

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On September 26 2001, an earthquake in North Bay measured 5.0 on the Ritcher scale. What is the magnitude of an earthquake 3 times as intense as North Bay's earthquake?


I would post my answer, but in text, it's just confusing and I can't post picture links to show my work...


Btw, the answer is 5.477

  • Math - Working with Logs!! - ,

    In 1935 C.F. Richter set up the scale of earthquakes by
    R = log(I) where R is the Richter scale number and I is the intensity of the earthquake

    so from your data
    5 = log(I)
    I = 10^5

    so an earthquake 3 times as intense would be 3I
    so multiplying the above equation by 3
    3I = 3(10^5)
    log (3I) = log(3*10^5)
    = log 3 + log 10^5
    = .47712 + 5
    = 5.47712

  • Math - Working with Logs!! - ,

    So, you don't use the equation:

    M = log(I_i / I_o) ?

  • Math - Working with Logs!! - ,

    most texts, and the one that I used last, use the formula

    R = log(I/I0) where 0 is a constant, the minimum intensity corresponding to R = 0

    so if you want

    5 = log (I/I0)
    5^10 = I/I0
    3*5^10 = 3I/I0
    log(3*5^10 = log(I/I0)

    notice it has no effect on the answer

  • Math - Working with Logs!! - ,

    i don't get where the 3 goes in the second line of this part :

    log (3I) = log(3*10^5)
    = log 3 + log 10^5

  • Math - Working with Logs!! - ,

    You have it right in the second line in the laws of logarithms a*b ends up equaling log 3 + log 10^5

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