The magnitudes of an earthquake is measured relative to the strength of a \"stan

Question

The magnitudes of an earthquake is measured relative to the strength of a "standard" earthquake, whose cosmic waves are of size W_0. The magnitude, M, of an earthquake with waves of size W is defined to be M = log_m(W W_0). The value M is called the Richter scale rating of the strength of the earthquake. Let M and m represent the magnitude of two earthquakes whose selsmic waves are of sizes W and w, respectively. Using properties of logarithms, find a simplified formula for the difference M - m, in terms of W and w.

Explanation / Answer

a)
M = log10 (W/Wo)
m = log10 (w/Wo)
M-m = log10 (W/Wo) - log10 (w/Wo)

use: log (a/b) = log a - log b

so,
M-m = log10 (W/w)
This is the answer Wo and Wo cancel each other

b)
use:
M-m = log10 (W/w)
8.7-6.9 = log 10 (W/w)
log 10 (W/w) = 1.8
W/w = 63.1

It is 63.1 times larger

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