Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 488: 20



Work Step by Step

RECALL: (i) If $a^M=a^N$, then $M=N.$ (ii) $(a^m)^n=a^{mn}.$ Write 8 and 4 as powers of 2: $8^{1-x} = 4^{x+2} \\(2^3)^{1-x}=(2^2)^{x+2}.$ Use rule (ii) above to obtain $2^{3(1-x)} = 2^{2(x+2)} \\2^{3-3x} = 2^{2x+4}.$ Use rule (i) to obtain $3-3x=2x+4.$ Solve the equation to obtain $3-4=2x+3x \\-1=5x \\\dfrac{-1}{5}=x.$
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