How many times more powerful is an earthquake measuring 53 o

How many times more powerful is an earthquake measuring 5.3 on the Richter scale than an earthquake measuring 4.2 on the Richter scale? Round your answer to three decimal places.

Solution

magnitude M =(I/S) where I is intensity of earth quake ,S is standard intensity

5.3 =log(I₁/S)

4.2 =log(I₂/S)

log(I₁/S) -log(I₂/S) =5.3-4.2

log a -log b =log(a/b)

log((I₁/S)(I₂/S)) =1.1

log(I₁/I₂) =1.1

(I₁/I₂) =10^1.1

(I₁/I₂) =12.589

I₁=12.589I₂

earth quake measuring 5.3 is 12.589 times stronger than earth quake measuring 4.2