pre calc question

Question

One earthquake has MMS magnitude 4.2. If a second earthquake has 690 times as much energy (earth movement) as the first, find the magnitude of the second quake.

Answer 1

The formula for MMS is MMS = (2/3)*log(S/S0) The log is base 10.

(2/3)*log(S/S0) = 4.2

For the 690 times as much energy quake it's (2/3)log(690S/S0) = (2/3)log(690 * S/S0) = (2/3)log(S/S0) + (2/3)log(690) = 4.2 + (2/3)log(690) = about 6.09