The magnitude M of an earthquake is measured using the formula M=log (x/c), where x is the measured amplitude of a seismic wave and c is the reference amplitude of one micron. Two earthquakes are measured. The amplitude of a seismic wave in the first earthquake is 80 times the amplitude of a seismic wave in the second earthquake. How much greater is the magnitude of the first earthquake than the second earthquake?

Question

Harper Ellis

Mathematics

6 June, 18:54

The magnitude M of an earthquake is measured using the formula M=log (x/c), where x is the measured amplitude of a seismic wave and c is the reference amplitude of one micron. Two earthquakes are measured. The amplitude of a seismic wave in the first earthquake is 80 times the amplitude of a seismic wave in the second earthquake. How much greater is the magnitude of the first earthquake than the second earthquake?

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Answers (1)

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Hadassah Leblanc · Answer 1

The first earthquake is 1.9 times greater than the second

Step-by-step explanation:

We need to substract

M1 and M2

M1 - M2 = ㏒ (x1/c) - ㏒ (x2/c)

by properties of the logarithm

= log (x1) - log (c) - (log (x2) - log (c))

= log (x1) - log (x2)

But, we know that x1 = 80*x2

So,

= log (80) + log (x2) - log (x2)

= 1.903