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ishpiro | College Teacher | (Level 1) Educator

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To find the magnitude of the earthquakes on the Richter scale, plug in the values for the energy released into the formula:

`M = 2/3 log(E/E_0)` ,

where `E_0 = 10^4.4` Joules. In this formula, log is the logarithm with the base of 10.

For the first earthquake, `E = 6*10^16` Joules, so

`E/E_0 = (6*10^16)/(10^4.4) = 6*10^11.6` (subtract the exponents when dividing the powers with the same base.)

`M = 2/3 log(6*10^11.6) =8.25 ` (rounded to two decimal places.)

The magnitude of the first earthquake is 8.25 on the Richter scale.

For the second earthquake, `E =1.25 *10^15` Joules, so

`E/E_0 = (1.25*10^15)/10^4.4 = 1.25*10^10.6`

`M = 2/3 *log(1.25*10^10.6) = 7.13`

The magnitude of the first earthquake is 7.13 on the Richter scale.

To compare the energy released in the two earthquakes, divide the energy released in the first earthquake by the energy released in the second one:

`(6*10^16)/(1.25*10^15) = 6/1.25 *10 = 4.8*10 = 48` (again, subtract exponents when dividing the powers of 10.)

The first earthquake released 48 times more energy than the second one.