Question

The magnitude, M, of an earthquake is defined to be M = log StartFraction I Over S EndFraction, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. Which equation represents the magnitude of an earthquake that is 10 times more intense than a standard earthquake?

Answer 1

the answer is 3

Explanation:

M=log1000 times the intensity over s for standard

if the intensity is standard then it will cancel out the top part, for example

log1000(s)/(s)

so your answer is just the log of 1000 which equals 3

Answer 2

C: M = log(10S/S)

Explanation:

We know that 'I' is the intensity of the earthquake based on its wave amplitude and S is the magnitude of a standard earthquake.

If we want to calculate the magnitude of an earthquake that is 10 times bigger than the standard one then we do the following operation:

I = 10S (i) (because the intensity is 10 times that of the standard earthquake)

Now:

M = log (I / S) (ii)

Replace (i) in (ii)

M = log (10S / S)