Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.7 - Common Logarithms, Natural Logarithms, and Change of Base - Exercise Set: 60

Answer

3.5

Work Step by Step

We are given that the formula $R=log(\frac{a}{T})+B$ can be used to find the intensity R of an earthquake on the Richter scale (where a is the amplitude in micrometers, T is the time in seconds between waves, and B is a constant). In this case, $a= 150$, $T=3.6$, and $B=1.9$. We can plug in these values to find R. Recall that $log(\frac{a}{T})$ is written in the form of the common logarithm and has a base of 10. $R=log(\frac{150}{3.6})+1.9=log(41.67)+1.9=1.6+1.9=3.5$
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