Question 1171054
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.