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  1. MHB Apprentice

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    #1
    Hello. I am doing a review sheet for my Pre-Calculus final and one of the questions has me stumped. I'm going through our notes and we never did a problem like this in class. Any help would be greatly appreciated. Thank you.

    Find the Richter scale magnitude of an earthquake that releases energy of $ \displaystyle E= 1000 E_0$ . Then find the energy released by an earthquake that measures 5.0 on the Richter scale given that that $ \displaystyle E_0$= $ \displaystyle 10^{4.40}$. Finally find the ratio in energy released between an Earthquake that measures 8.1 on the Richter scale and an aftershock measuring 5.4 on the scale. Use the formula R = 2/3 log E/Eo

    A) R = 2, E = 7.94 x $ \displaystyle 10^{11}$ joules and the ratio E1/E2 = 10200/1
    B) R = 2, E = 7.94 X $ \displaystyle 10^{10}$ joules and the ratio E1/E2 = 11200/1
    C) R = 2, E = 7.94 X $ \displaystyle 10^{11}$ joules and the ratio E1/E2 = 11200/1
    D) R = 3, E = 7.94 X $ \displaystyle 10^{11}$ joules and the ratio E1/E2 11200/1
    E) R = 2, E= 5.94 X $ \displaystyle 10^{11}$ joules and the ratio E1/E2 = 11200/1

    Which answer would be the correct one?

  2. Pessimist Singularitarian
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    #2
    We are told to use the formula:

    $ \displaystyle R=\frac{2}{3}\log\left(\frac{E}{E_0}\right)\tag{1}$

    For the first earthquake we are given, we are told $E=1000E_0=10^3E_0$. So, plugging this into (1), there results:

    $ \displaystyle R=\frac{2}{3}\log\left(\frac{10^3E_0}{E_0}\right)=\frac{2}{3}\log\left(10^3\right)$

    Now, using the identities $\log_a\left(b^c\right)=c\log(b)$ and $\log_a(a)=1$, what do you find for $R$?

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