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Algebra

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Moderate

Applications of Logarithms - Earthquake Magnitude

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The Richter scale is commonly used to measure the intensity of an earthquake. There are many different ways of computing this, based on a number of different quantities.

If $E$ is the energy released (measured in joules) during an earthquake, then the magnitude of the earthquake is expressed as:

$$M =\frac{2}{3}\log(\frac{E}{E_0})$$

...where $E_0 = 10^{4.4}$ joules.

How much energy (in joules) will be released in an earthquake with a magnitude of 8.9?

Note: Recall that a joule is the amount of energy required to lift a small apple with a mass of approximately 100g vertically through one meter of air.

A

$ 10^{7.75}$

B

$ 10^{13.75}$

C

$ 10^{15.75}$

D

$ 10^{17.75}$