Question

The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8). Find the energy released by an earthquake of magnitude 4.2

Answer 1

Just substitute M=4.2 in the given equation. Make the whole log term the subject.

$\log(\frac{E}{10^{11.8}})=\frac{3M}{2}$

Then, remove the log,:

$\frac{E}{10^{11.8}}=10^{\frac{3M}{2}} E=10^{11.8}\times10^{\frac{3\times4.2}{2}}=10^{11.8+6.3}=10^{18.1}=1,258,925,411,794,167,210$

Answer 2

4.2 = [2/3] log [E / 10^11.8 ]

4.2 * 3 / 2 = log E - log (10^11.8)

6.3 + 11.8 = log E

18.1 = log E

E = 10^18.1 erg.