Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 395: 35



Work Step by Step

$6(2^{3x-1})-7=9$ $6(2^{3x-1})=16$ $2^{3x-1}=\frac{16}{6}=\frac{8}{3}$ $\log_22^{3x-1}=\log_2\frac{8}{3}$ (Use the Inverse Property: $\log_aa^x=x$): $3x-1=\log_2\frac{8}{3}=\frac{\ln\frac{8}{3}}{\ln2}=\frac{\ln8-\ln3}{\ln2}$ $3x=\frac{\ln8-\ln3}{\ln2}+1$ $x=\frac{\frac{\ln8-\ln3}{\ln2}+1}{3}=0.805$
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