As we know, logarithms were developed to help mathematicians and scientists deal with and do calculations with very large (or very small numbers) numbers. Logarithmic scales are still often used in place of measurements when the range of measurement is very large, as in starlight, earthquake or sound intensity.
Charles Richter, a seismologist, invented the Richter scale for measuring the strength of an earthquake.
M is the amount of ground movement (strength of the earthquake) and R is the strength of the earthquake on the Richter scale. This scale is given by
R
 log M
Remember: When no base is indicated, the log is a common logarithm with base 10. In other words,
R
 log M is the same as R
 log
10
M
Problem #1 : The 1906 earthquake in San Francisco measured 8.4 on the Richter scale. The October,
1987 earthquake in Los Angeles measured 6.1 on the Richter scale. How many times more powerful, in terms of ground movement, was the 1906 earthquake than the 1987 earthquake?
Problem #2 : Another source I checked said that the 1906 San Francisco earthquake had a Richter scale of 8.3 rather than 8.4. How many times more powerful, in terms of ground movement, is an 8.4 quake than an 8.3 quake? Does the difference seem inconsequential or important? Explain.
The amount of energy (E) released in an earthquake can be approximated by the equation log
31
E

R
, where R is the Richter scale measurement of the earthquake.
Problem #3 : Given this information, how much more energy is there in an earthquake that registers 3 on the Richter scale than one that registers 5?
Problem #4 : How much more energy is there in an earthquake that registers 3 on the Richter scale than one that registers 7?