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CalculusQ&A LibraryThe magnitude, M, of an earthquake, is represented by the equation M=2/ 3 log (E/ E 0) where E is the amount of energy released by the earthquake in joules and E0=10 4.4 is the assigned minimal measure released by an earthquake.To the nearest tenth, what would be the magnitude of an earthquake releasing 2.1⋅10 14 joules of energy?Question

Asked Mar 21, 2019

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The magnitude, M, of an earthquake, is represented by the equation M=2/ 3 log (E/ E _{0}) where E is the amount of energy released by the earthquake in joules and E0=10 ^{4.4} is the assigned minimal measure released by an earthquake.

To the nearest tenth, what would be the magnitude of an earthquake releasing 2.1⋅10^{14} joules of energy?

To the nearest tenth, what would be the magnitude of an earthquake releasing 2.1⋅10

Step 1

**Introduction:**

Denote the magnitude of an earthquake as *M.*

Denote the amount of energy released by the earthquake in joules as *E.*

Denote the assigned minimal measure released by an earthquake as *E*_{0}.

The formula to find the magnitude of an earthquake is,

Step 2

**Obtain the magnitude of an earthquake releasing 2.1*10 ^{14 }joules of energy:**

Here, it is given that the assigned minimal measure released by an earthquake is *E*_{0} = 10^{4.4}.

The amount of energy released by the earthquake in joules is *E* = 2.1*10^{14}.

The magnitude of an earthquake releasing 2.1*10^{14 }joules of energy is obtained as **0 **from the calculation given below:

Step 3

**Obtain the magnitude of an earthquake releasing 2.1*1014 joules of energy (With base 10):**

Here, it is given that the assigned minimal measure released by an earthquake is *E*0 = 104.4.

The amount of energy released by the earthquake in joules is *E* = 2.1...

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