One earthquake has magnitude 4.5. If a second earthquake has 760 times as much energy as the first, find the magnitude of the second quake.

Question

anonymous · Answer

@whpalmer4

john_es · Answer

I think this can be a solution. Suppossing, 
$$Magnitude \propto log_{10}(Energy)$$ Then if M=4.5, the second quake has magnitude,
$$M=\log_{10}(750\cdot Energy)=\log_{10}750+\log_{10}(Energy)=\log_{10}750+4.5\approx 7.38$$

john_es · Answer

Oh, change the 750 for the correct number, 760 and redo the calculus.

anonymous · Answer

I think they want me to use the formula M = 2/3log(S/S0)

anonymous · Answer

7.38 was not the solution

john_es · Answer

Yes, because I use 750. Using your equation and the reasoning before, you have,

$$M=4.5+2/3\log_{10}(760)\approx 6.42$$

anonymous · Answer

That is right.  Thanks :)

john_es · Answer

You're welcome. ;)