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?
M = log StartFraction I Over S EndFraction
M = log (10 S)
M = log StartFraction 10 S Over S EndFraction
M = log StartFraction 10 Over S EndFraction

Answer 1

If the earthquake is 10 times as intense as the standard, I = 10S. Substitute into M = log(I/S):

M = log((10S)/S)

This simplifies to M = log(10) = 1. So the correct equation is M = log((10S)/S).