Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Review Exercises - Page 512: 47


The simplified value is $ R=3$.

Work Step by Step

We know that the intensity of the earthquake is represented by $1000{{I}_{o}}$. So, $ I=1000{{I}_{o}}$ Put the value of I in $ R=\log \left( \frac{I}{{{I}_{o}}} \right)$, $\begin{align} & R=\log \left( \frac{1000{{I}_{o}}}{{{I}_{o}}} \right) \\ & =\log \left( 1000 \right) \end{align}$ As ${{10}^{3}}=1000$ Rewrite the above exponential form with logarithms: If ${{b}^{y}}=x $, then ${{\log }_{b}}x=y $, Then, ${{10}^{3}}=1000$ is equivalent to $\log \left( 1000 \right)=3$. Thus, the magnitude on the Richter scale is $ R=3$.
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