The Richter scale for earthquakes is as follows:  if I is the intensity of an earthquake and I₀ is the intensity of the shaking without an earthquake, then the magnitude R of an earthquake is defined by  

        R = log[I/I₀]

The Loma Prieta quake measured 7.1 on the Richter scale and the Hokkaido quake measured 8.2.  How many times more intense was the Hokkaido quake?

Solution

Let 

        I_L = The intensity of the Loma Prieta quake

and

        I_H = The intensity of the Hokkaido quake

        We write

        log(I_H/I_L)  = log(I_H/I₀ / I_L/I₀)

        =  log(I_H/I₀) – log(I_L/I₀)

        =  8.2 – 7.1  =  1.1

By exponentiating both sides with base ten, we get

        I_H/I_L  = 10^1.1  =  12.6

We can conclude that the Hokkaido quake was more than 12 times more intense than the Loma Prieta quake.