Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 73



Work Step by Step

$8^{-x+14}=(2^3)^{-x+14}=2^{-3x+42}$, $16^x=(2^4)^x=2^{4x}$ hence the equation becomes: \begin{align*}2^{-3x+42}=2^{4x}.\end{align*} The base is same on the 2 sides on the equation (and it is not $1$ or $-1$), hence they will be equal if the exponents are equal. Hence $-3x+42=4x\\42=7x\\x=6$.
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