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### 1 Answer

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.**