pls solve my precalculus word problem. ASAP. Use steps below to solve.

Mathematics
Tutor: None Selected Time limit: 1 Day

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. 

Sep 1st, 2015

Thank you for the opportunity to help you with your question!

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




Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 1st, 2015

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