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?
IL = The intensity of the Loma Prieta quake
IH = The intensity of the Hokkaido quake
log(IH/IL) = log(IH/I0 / IL/I0)
= log(IH/I0) – log(IL/I0)
= 8.2 – 7.1 = 1.1
By exponentiating both sides with base ten, we get
IH/IL = 101.1 = 12.6
We can conclude that the Hokkaido quake was more than 12 times more intense than the Loma Prieta quake.