Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.5 Logarithmic Functions - 2.5 Exercises - Page 98: 62

Answer

$x \approx 2.262$

Work Step by Step

$2^{x+1}=6^{x-1}$ $\ln 2^{x+1}=\ln 6^{x-1}$ $(x+1) \ln 2 = (x-1) \ln 6$ $(\ln 2)x + \ln2 = (\ln 6) x- \ln 6$ $\ln 2 + \ln 6 = (\ln 6 - \ln 2)x$ $x = \frac{\ln 2 + \ln 6}{\ln 3} \approx 2.262$
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