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: 70



Work Step by Step

Re-write the given equation as: $(2^2)^{x^2}=2^{2x^2}$ or, $2^{2x^2}=2^{x}$ 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, $ 2x^2=2x \\ 2x^2-x=0 \\ x(2x-1) =0 $ By the zero property rule, we have: $x=0$ and $2x-1=0 \implies x=0.5$
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