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: 42


$x \approx 0.188$

Work Step by Step

First, divide both sides by $4$ to get $$13^{3x}=\frac{17}{4}$$ Take the natural log of both sides to get $$\ln 13^{3x} = \ln (17/4)$$ Since $\ln a^b=b \ln a$, the equation becomes $$3x \ln 13 = \ln (17/4)$$ Divide both sides by $3\ln 13$ to get $$x=\frac{\ln (17/4)}{3 \ln 13}\approx0.188$$
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