Description
The Richter scale is used to measure the magnitude of a earthquake. The magnitude, R, is given by the equaiton R=0.65log(0.39E)+1.45, where E is the energy (measured in kilowat hours)released by the earthquake. Determine the amount of energy released by an earthquake of magnitdude 7.5
USE THESE STEPS TO SOLVE:
a. Rewrite equation for magnitude of earthquake, using magnitude of 7.5 given in problem.
b. Simplify so it is writen in form b=loga
c.solve problem for E, the energy released in earthquake.
Explanation & Answer
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a. You're given the main equation where R is the magnitude of the earthquake. This part just asks you to substitute 7.5 in for R in the main equation:
R=0.65log(0.39E)+1.45
7.5=0.65log(0.39E)+1.45
b. Now you need to simplify the expression into the form b=loga
6.05=0.65log(0.39E) Subtracted 1.45 from both sides of equation.
9.31=log(0.39E) Divided each side by 0.65. That's the answer to part b.
c. To solve for E, you need to get the E out from within the log function. You can use a simple 'log rule' to do this:
General rule:
log(x)=N can be rewritten as 10^N=x
To rewrite the main equation:
9.31=log(0.39E)
10^(9.31)=0.39E
E=5.24*10^9 kilowatt hours
Review
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