Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 488: 22

Answer

$x = \dfrac{-4}{3}$

Work Step by Step

RECALL: (i) If $a^M=a^N$, then $M=N.$ (ii) $\dfrac{1}{a^m} = a^{-m}.$ Use rule (ii) above to obtain $e^{x+4} = e^{-2x}.$ Use rule (i) to obtain $x+4 = -2x.$ Solve the equation: $x+4+2x=-2x+2x \\3x+4=0 \\3x+4-4=0-4 \\3x=-4 \\x = \dfrac{-4}{3}.$

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