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# ​ Help (Logarithmic Expressions and Earthquake Magnitudes)

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I was doing this question for a homewokr assignment and don't understand how to solve this beacuse the value of S is never given. Please Help.

Here's the question if the picture doesn't show:

The Ritcher Scale is a scale created by Charles Ricther to measure the magnitude of earthquakes. The magnitude, M, of any given earthquake is defined by the ritcher scale as:    M = log(I/S)

...where I is the intensity (which is defined as the amplitude of the serismograph reading taken 100km from th eepicenter of the earthquake), and S is considered to be the intensity of a standard earthquake.

In the year 1950, the strongest earthquake recorded was in india and had a magnitude of 8.6 on the ricther scale. The tenth strongest recorded earthquake was in the Phillippines and had a magnitude of 7.0 on the Ritcher Scale.

How much stronger was the 1950 earthquakes Intensity than the Phillippines earthquakes intensity?

Dec 15, 2019
edited by Krypticsx  Dec 15, 2019

#3
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M1 = 8.6 = log (i1/s)

10^(8.6) = i1/s

M2 = 7.0 = log (i2/s)

10^7 = I2/s

M1/M2 = 10^8.6/10^7 = i1/i2       10^1.6 = i1/i2     39.8 = i1/2      i1 was 39.8 times more intense than i2   (not positive about this)

Anyone else have a different answer?

Dec 15, 2019

#1
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I don't see anything in the picture....

Dec 15, 2019
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Go online to this page and enter 8.6 magnitude and 7 magnitude and compare the the two in Intensity, Energy release, Seismic moment.....etc.

https://www.wolframalpha.com/input/?i=+8.6+magnitude+Earthquake+Statistics&assumption=%7B%22FS%22%7D+-%3E+%7B%7B%22SeismicMomentMagnitudeToEnergy%22%2C+%22EJ%22%7D%7D&assumption=%7B%22F%22%2C+%22SeismicMomentMagnitudeToEnergy%22%2C+%22Mw%22%7D+-%3E%227%22

Dec 15, 2019
#3
+19820
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M1 = 8.6 = log (i1/s)

10^(8.6) = i1/s

M2 = 7.0 = log (i2/s)

10^7 = I2/s

M1/M2 = 10^8.6/10^7 = i1/i2       10^1.6 = i1/i2     39.8 = i1/2      i1 was 39.8 times more intense than i2   (not positive about this)

Anyone else have a different answer?

ElectricPavlov Dec 15, 2019
#4
+106539
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Correct, EP!!!

I just use this formula

d = 10^(8.6 - 7)  = 10^(1.6)  ≈  39.8  times as great