Using logarithm to find earthquake strength

• March 30th 2009, 01:34 AM
vidalex
Using logarithm to find earthquake strength
Word Problem that I'm stuck on
The common logarithm is used to measure the intensity of an earthquake on the Richter scale. The Richter scale rating of an earthquake of intensity I is given by log(I) - log(Io), where Io is the intensity of a small "benchmark" earthquake. Write the Richter scale rating as a single logarithm. What is the Richter scale rating of an earthquake for which I = 1000*Io?
• March 30th 2009, 02:23 AM
mathsquest
log (I/I0). For the second part, log1000
• March 30th 2009, 04:02 AM
mr fantastic
Quote:

Originally Posted by vidalex
Word Problem that I'm stuck on
The common logarithm is used to measure the intensity of an earthquake on the Richter scale. The Richter scale rating of an earthquake of intensity I is given by log(I) - log(Io), where Io is the intensity of a small "benchmark" earthquake. Write the Richter scale rating as a single logarithm. What is the Richter scale rating of an earthquake for which I = 1000*Io?

You should know the rule $\log A - \log B = \log \frac{A}{B}$.