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oksian1 [2.3K]
3 years ago
11

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?
Mathematics
1 answer:
klemol [59]3 years ago
7 0

Answer:

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

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