Earthquake magnitude

Question

Could someone please help me with this question?

An earthquake has magnitude 6.7 and its aftershock has magnitude 4.7 on the base 10 logarithmic Richter scale. How much larger is the first earthquake?

Answer 1

10^6.7 = 5,011,872.3= about 5 million

10^4.7 = 50,118.7 = about 50 thousand

5 million is 100 times 50 thousand

5,011,872.3/50.118.7 = 100.00005 = virtually 100 =100 but for rounding errors

6.7-4.7 = 2

10^2 =100 times difference