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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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