Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 57

Answer

$8.3$

Work Step by Step

As per the given problem, the magnitude of an earthquake $=log_{10}(\frac{I}{S})$ Where, I is the intensity of the quake (measured by the amplitude of a seismograph 100 km from the epicenter) and S is the intensity of a “standard” earthquake (where the amplitude is only 1 micron=$10^{-4}$ cm) The magnitude of earthquake on the Richter scale in year 1989 = 7.1 Therefore, $log_{10}(\frac{I}{S})=7.1$ The intensity of earthquake was 16 times as intense in the year of 1906. Therefore, the magnitude of earthquake $=log_{10}(\frac{16I}{S})$ Now, $log_{10}(\frac{16I}{S})=log_{10}16+log_{10}(\frac{1}{S})$ $log_{10}(\frac{16I}{S})=log_{10}16+7.1$ Hence, $log_{10}(\frac{16I}{S})= 8.3$
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