Question 252183: An earthquake registers 6.1 on the Richter scale. What is the rating on an earthquake that is twice as powerful?
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! Richter numbers are based on powers of 10. For example a 7.1 will be 10 time more powerful than a 6.1. Put another way 1og^(7.1-6.1) = 10^1 = 10. Our task is to find what magnitude makes a 2, not a 10. Here we go . . .
log_10(X) = (a-b) -> in words log_10 = log base 10
Since we have a magnitude of 6.1, and want an EQ twice as strong,
log_10(2) = (a-6.1)
10^(a-6.1) = 2
By log of both sides,
a - 6.1 ~ .30103
a ~ 6.4.
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