LSP 121
Homework 5: Logs and Richter Scale, Decibels

Open the file logs.xls (found on the QRC website under Excel Files). You will use this file for both parts below. Click on the worksheet tabs at the bottom to access the other file. 1. Richter scale
The Richter scale is used to measure the intensity of earthquakes. It is a logarithmic relationship with the following formula: R = log(I) I is the intensity of the earthquake and R is the number on the Richter scale.
(Remember that if there is no base written with the log it is base 10).
Don’t be scared off by logs. Think of them as a short-cut way of writing large numbers. For example, let’s say the intensity of an earthquake is 100,000,000. Can you imagine if the papers published that big number? What would people think? Most people cannot handle well numbers with large amounts of zeros (unless those people work for the government ;-). Instead of writing 100,000,000, let’s just write how many zeros there are. In this case, there are 8 zeros. That’s exactly what log10 is asking. 10 to what power equals 100,000,000? 10 to the 8th power. So the log(100,000,000) equals 8. Thus, the Richter value for an earthquake with intensity 100,000,000 is 8.
Let’s say it another way. Let’s remove the log. Converting the above formula from log form to exponent form would give us:
10R = I
(Note: 10 was raised to the R power, which cancels the log function.) Which version you use depends on which variable you are given. If you are given the Richter value (R) and want to calculate the intensity, then use 10R = I. If you are given the intensity and want to calculate the R value, use R = log(I).
Since the Richter scale is logarithmic, an increase of 1 on the Richter scale translates to 10 times increase in intensity. An R of 2 means an intensity of 100 while an R or 3 has an intensity of 1000 which