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?

The magnitude of the first earthquake is 2 more than the second earthquake

The function is given as:

And the relationship between the amplitudes is given as:

Assume the magnitudes are M1 and M2.

So, the function can be rewritten as:

Subtract M2 from M1

Apply the quotient property of the logarithm

Expand

Evaluate the common terms

Substitute

Apply the product property of logarithm

Evaluate the common terms

Evaluate log(80)

Approximate

Hence, the magnitude of the first earthquake is 2 more than the second earthquake

Read more about logarithmic functions at:

link

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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