Question 1043516: The Magnitude, M, of an earthquake is measured using Richter scale: M= log(I/I_0). A "great" earthquake measures about 8 on the scale, while a "light" earthquake measures about 4. Does this mean that a great earthquake is twice as intense as a light earthquake? If so, explain why, and if not, explain why not, using mathematical reasoning.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! M=log (I/Io)
10^M=I/Io
Let M=4
10000=I/Io
I=10000*Io
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now let M=8
10^8=I/Io
100,000,000=I/Io
I=100,000,000*Io
The second earthquake is 10^8/10^4 stronger, or 10,000 times stronger.
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Twice as strong would be
I=20,000*Io
I/Io=20,000
log (I/Io)=log (20,000)=4.30
an earthquake of magnitude 4.30 would be twice as strong as one that has magnitude 4.
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