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The magnitude, m, of an earthquake is represented by the equation m=23logee0 where e is the amount of energy released by the earthquake in joules and e0=104.4 is the assigned minimal measure released by an earthquake. which equation could be used to find the amount of energy released by an earthquake with a magnitude of 2.7?

Sagot :

An earthquake's energy output when it has a magnitude of 2.7 is 4.5 × [tex]10^{12}[/tex].

The magnitude of an earthquake is the most common indicator of its size. It serves as a barometer for the size of an earthquake's single source. Because it is the same no matter where and how you see it, the following calculation may be done:

magnitude, M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

Where E is the power generated in Joules and M is the lowest magnitude emitted by such an earthquake, [tex]E_{0} = 10^{4.4}[/tex].

Assuming 5.5, the same magnitude is provided when the preceding equation is used:

M = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

5.5 = 2 ÷ 3 log(E ÷ [tex]E_{0}[/tex])

8.25 = [tex]log(\frac{E}{10^{4.4}})[/tex]

[tex]10^{8.25}[/tex] = [tex]\frac{E}{10^{4.4}}[/tex]

E = [tex]10^{4.4}[/tex] × [tex]10^{8.25}[/tex]

E = 4.5 × [tex]10^{12}[/tex]

Therefore the final answer is 4.5 × [tex]10^{12}[/tex].

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