Final answer:
The earthquake's magnitude that is 100 times more intense than a standard earthquake is represented by the equation M = log(100S) using a logarithmic scale.
Step-by-step explanation:
The magnitude of an earthquake is determined using a logarithmic scale, specifically the Richter scale, which is based on the logarithm of the amplitude of the earthquake waves. To represent an earthquake that is 100 times more intense than a standard earthquake, we use the equation:
M = log(100S)
where M stands for magnitude, log indicates the logarithm base 10, and S denotes the standard amplitude. Since the Richter scale is logarithmic, each whole number increase represents a tenfold increase in amplitude. Thus, 100 times more intense translates to 2 logarithmic units since 10² = 100.