College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.7 - Logarithmic Scales - 4.7 Exercises - Page 422: 11

Answer

Larger by: $\log{20}\approx 1.3$

Work Step by Step

We know that $M=\log\frac{I}{S}$ and thus $10^M=\frac{I}{S}$ Hence, here if $I_1,I_2$ are the intensities, where $I_1=20I_2$, we have (by the product rule for logarithms): $M_1=\log\frac{20I_2}{10^{-4}}=\log\frac{I_2}{10^{-4}}+\log{20}=M_2+\log{20}\approx 1.3$ (magnitude larger)
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