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 - Exercises to Skills for Chapter 5 - Page 232: 46


$x \approx 113.8$

Work Step by Step

First, add $6$ to both sides to get $$3\log(4x+9)=8$$ Next, divide both sides by $3$ to get $$\log(4x+9)=\frac{8}{3}$$ Since $10^a=10^b$ if $a=b$ and $10^{\log a}=a$, $$4x+9=10^{8/3}$$ Subtract $9$ from both sides to get $$4x=10^{8/3}-9$$ Divide both sides by $4$ to get $$x=\frac{10^{8/3}-9}{4}\approx113.8$$
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