The Richter scale is used for measuring the magnitude of an

The Richter scale is used for measuring the magnitude of an earthquake. The Richter magnitude is given by R = 0.67 log (0.37E) + 1.46 where E is the energy (in kilowatt-hours) released by the earthquake. How many kilowatt-hours of energy would an earthquake have to release in order to be an 8.5 on the Richter scale?

Solution

R = 0.67 log (0.37E) + 1.46

8.5=0.67 log (0.37E) + 1.46

8.5 - 1.46 = 0.67 log (0.37E)

7.04 = 0.67log (0.37E)

log (0.37E) =7.04/0/67 =10.57

0.37E = e^10.57

0.37E = 36587.5275

E= 98885.2096 Killowatt hours