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: 47


$x \approx 1.625$

Work Step by Step

First, add $5$ to both sides to get $$4\log(9x+17)=6$$ Next, divide both sides by $4$ to get $$\log(9x+17)=\frac{6}{4}=\frac{3}{2}$$ Since $10^a=10^b$ if $a=b$ and $10^{\log a}=a$, $$9x+17=10^{3/2}$$ Subtract $17$ from both sides to get $$9x=10^{3/2}-17$$ Divide both sides by $9$ to get $$x=\frac{10^{3/2}-17}{9}\approx1.625$$
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