Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 469: 23

Answer

$x=9.386$

Work Step by Step

The given expression can be written as: $ e^{3x-7-2x}=4e $ This implies that $ e^{x-7} =4e$ We need to take natural log of both sides and apply logarithmic property : $\log a^ b=b \log a$ . $(x-7) \ln e=\ln 4e$ Now, we will evaluate the result for $x$. $x-7 =2.386$ Therefore, our answer is: $x=9.386$
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