Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 71



Work Step by Step

Re-write the given equation as: $(2^3)^{-x+14}=(2^4)^x$ or, $2^{-3x+42}=2^{4x}$ Use the rule power rule: $a^p=a^q$. We can see that the base $a=2$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $ -3x+42=4x \\ 7x=42 \\ x =6$
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