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: 19

Answer

$x=13$

Work Step by Step

RECALL: (i) If $a^M=a^N$, then $M=N.$ (ii) $(a^m)^n=a^{mn}.$ Write 8 and 16 as powers of 2 to obtain $8^{x+3} = 16^{x-1} \\(2^3)^{x+3}=(2^4)^{x-1}.$ Use rule (ii) above to obtain $2^{3(x+3)} = 2^{4(x-1)} \\2^{3x+9} = 2^{4x-4}.$ Use rule (i) to obtain $3x+9=4x-4.$ Solve the equation to obtain $9+4=4x-3x \\13=x.$
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