Question 1171054: The magnitude of an earthquake in san Luis Aurora province in May 2020 is 5.4. And it is predicted that there will be another earthquake that will strike somewhere in the philippines that is 5 times stronger than the mentioned earthquake. What could be the possible magnitude of the predicted earthquake? (Use Earthquake magnitude on a Richter scale R=2/3logE/10^4.40
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference from brainly.com
On the Richter scale, the magnitude, M, of an earthquake is given by M= 2/3logE/Eo, where E is the energy released by the earthquake measured in joules, and Eo is the energy released by a very small reference earthquake. Eo has been standardized to 10^4.4 joules.
the formula is:
R = 2/3 * log(E/10^4.4)
i believe M in their formula and R in your formula mean the same thing.
R is the magnitude on the richter scale.
E is the energy released by the earthquake.
E0 is the energy release by a reference earthquake.
the value for E0 is equal to 10^4.4.
in your problem, M is equal to 5.4 which i translated to R = 5.4.
the formula becomes 5.4 = 2/3 * log(E/10^4.4)
multiply both sides of this equation by 3/2 to get:
5.4 * 3/2 = log(E/10^4.4)
simplify to get:
8.1 = log(E/10^4.4)
since log(E/10^4.4) = log(E)-log(10^4.4), the equation becomes:
8.1 = log(E) - log(10^4.4)
add log(10^4.4) to both sides of the equation to get:
8.1 + log(10^4.4) = log(E)
solve for log(E) to get:
log(E) = 8.1 + log(10^4.4) = 12.5
this is true, if and only if 10^12.5 = E.
you have:
E = 10^12.5
if another earthquake is 5 * stronger, than the mentioned earthquake, then that earthquake will have E = 10^12.65 + 5*10^12.65 = 6 * 10^12.65.
to find the magnitude of this earthquake, go back to the formula to get:
R = 2/3 * log(6*10^12.5/10^4.4) = 5.9187675.
if i did this correctly, your answer should be that the magnitude of the earthquake that is 5 times stronger will be 5.9187675.
i simply followed the guidelines provided by the reference.
note that when something is 5 times stronger, it is 6 times as strong.
x + 5x = 6x.
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