Title:  Earthquake Intensity     

Problem:  The Richter scale for measuring the intensity of earthquakes has been used since its inventions in 1932 by Charles F. Richter (1901-1985).  The scale has a property that its values are common logarithms.  The Japanese earthquake of 1923 is estimated to have measured 8.9 on the Richter scale.  The 1906 San Francisco earthquake is estimated to have measured 8.3.  If log x = 8.9 and log y = 8.3, x is how many times as big as y?  (This gives you an idea of how much more intense the Japanese earthquake was.)

Math Topic/Concept:  Logarithms, Exponents

Materials:  none

Classroom Use: Evaluation

Classroom use comments:  This problem is useful to determine if students understand how to change logarithms into exponents and then solve the problem.

Grade:   11 or 12

Grade Cluster: Late HS

Illinois Goal:  8

Standard: 8C5;   8B5

Applied? (1-4):  3:  This is a real world situation and one likely to occur if the person is interested in earthquakes and the Richter scale.

Source:  Function, Statistics, & Trig (p.239, #12).  UCSMP published by Scott Foresman (1992)

Answer:  about 4 times as great

Strategies Listed:  Change logarithms into exponent, write equation & substitute values, then solve.

Solution:  if log x = 8.9, then x = 10 ^ 8.9 and if log y = 8.3, then y = 10 ^ 8.3.  The problem also gives the equation x = (some value) times y.  With substitution you get the equation 10^ 8.9 = a (10 ^ 8.3).  Solving for a you get a = (10 ^ 8.9) / (10 ^ 8.3), therefore a≈ 4.

Other solution methods (if any): 

Extensions or related problems:  Have students research other earthquakes and compare any two they find.

Intended rubric or assessment method:  Assign 5 points: 3 for the correct answer and 2 for the work.

Notes (if any): 

Write-up submitted by:  Debby Hurt

James R. Olsen, Western Illinois University
E-mail: jr-olsen@wiu.edu
updated: June 30, 2005