Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.5 Apply Properties of Logarithms - 7.5 Exercises - Problem Solving - Page 512: 72


See below.

Work Step by Step

$L(I)=10\log\frac{I}{I_0}$ where $I_0=10^{−12}$. Hence here $L(I)_{whale}=10\log\frac{10^{6.8}}{10^{−12}}=10\log{10^{18.8}}=10\cdot18.8=188$ $L(I)_{human}=10\log\frac{10^{0.8}}{10^{−12}}=10\log{10^{12.8}}=10\cdot12.8=128$ Thus the whale can make a louder sound by $60$ decibels.
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