Question 1138533: The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula log(I1/I2)= M1 - M2
where M is the magnitude given by the Richter scale. An earthquake of magnitude 6.9 hit a city. Two years later, that same region experienced yet another, more devastating earthquake, this time with a magnitude of 9.0. How many times greater was the intensity of the second earthquake? Round to the nearest whole number.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 9.0 = log(M1) if and only if 10^9 = M1.
6.9 = log(M2) if and only if 10^6.9 = M2.
M1 / M2 = 10^9 / 10^6.9 = 10^(9 - 6.9) = 10^2.1 which means that M1 = 10^2.1 times as powerful as M2 which means that M1 = 125.8925412 times as powerful as M2.
the logarithmic scale works this way.
log(x) = y if and only if y = 10^x.
that's if the logarithmic scale is to the base of 10, which it is when you are dealing with the richter scale.
when applied to magnitudes of earthquakes, y is the magnitude of the earthquake and x is the intensity or the earthquake, or the amount of energy released by the earthquake.
an earthquake with a magnitude of 7 will be 10 times as powerful as earthquake with a magnitude of 6, based on the richter scale.
the magnitude of 7 will be related to the intensity by the formula y = log(x) where y is the magnitude and x is the intensity.
the intensity is a relative measure to earthwuakes of different magnitudes.
a magnitude 7 will be related to intensity by the formula 7 = log(x1).
a magnitude 6 will be related to intensity by the formula 6 = log(x2)
the log function is the inverse of the exponent function.
7 = log(x1) if and only if 10^7 = x1.
6 = log(x2) if and only if 10^6 = x2.
x1 is x1/x2 times as powerful as x2 = 10^7 / 10^6 = 10 times as powerful.
these measures are, by themselves, very simplistic and don't take into account the many factors that are used to measure the overall strength of an earthquake, but are a good basic definition of the relationship between magnitude and intensity on the richter scale.
the main point here is that the richter scale is a logarithmic scale and that every integer higher on the richter scale means that the power of the earthquake is 10 times as much as the next integer lower.
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