Eartquakes are, or more accurately, were meaured on Logarithmic Scale to base 10. That being the case, what is the amount of energy released, in Joules, by a Magnitude 8 earthquake, given this formula: M=2/3log(E/10^11.8), where M=Magnitude of the quake, E=Energy release in ergs. Thanks for any help.
+2592 8=(2log(E/10^11.8))/3
I'm going to assume that exponet is on 10
24=2log(E/10^11.8)
3 moved over
12=log(E/10^11.8)
Lets that the inverse of log which is B^E=L where B is the base, E is what is equal to the log, and L is the log
10^12=e/10^11.8
10^12*10^11.8 = 630957344480194300000000
e=6.3095*10^23 joules of energy
Solve for J: 8 = (2 log(1.58489×10^-12 J))/(3 log(10)) (2 log(1.58489×10^-12 J))/(3 log(10)) = (2 log(1.58489×10^-12 J))/(3 log(10)): 8 = (2 log(1.58489×10^-12 J))/(3 log(10)) 8 = (2 log(1.58489×10^-12 J))/(3 log(10)) is equivalent to (2 log(1.58489×10^-12 J))/(3 log(10)) = 8: (2 log(1.58489×10^-12 J))/(3 log(10)) = 8 Divide both sides by 2/(3 log(10)): log(1.58489×10^-12 J) = 12 log(10) 12 log(10) = log(10^12) = log(1000000000000): log(1.58489×10^-12 J) = log(1000000000000) Cancel logarithms by taking exp of both sides: 1.58489×10^-12 J = 1000000000000 Divide both sides by 1.58489×10^-12: Answer: | | J= 630957344480194367324160/10,000,000=63,095,734,448,019,436.7324160=6.31 X 10^16 Joules released in 8M earthquake. Since 1 Megaton H-bomb realses: 4.2 X 10^15 Joules, then an 8M earhquake will release:63/4.2=~15 Megatons of TNT equivalent
