Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 193: 33



Work Step by Step

Divide both sides by $17$ to get $$\frac{48}{17}=2.3^w$$ Next, take the natural log of both sides to get $$\ln \frac{48}{17}=\ln 2.3^w$$ Since $\ln a^b=b \ln a$, this equation simplifies to $$\ln \frac{48}{17}=w \ln 2.3$$ Divide both sides by $\ln 2.3$ to get a solution of $$w=\frac{\ln \frac{48}{17}}{\ln 2.3}\approx1.246$$
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