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: 75



Work Step by Step

Re-write the given equation as: $(2^2)^{x} \cdot 2^{x^2}=2^{8} ...(1)$ We know that $a^{m} \cdot a^n =a^{m+n}$ So, we can write equation (1) as: $2^{2x+x^2}=2^{8}$ 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, $2x+x^2=8 \\ x^2+2x-8=0 \\ (x+4)(x-2)=0$ By the zero-product property, we have: $x=-4,2$
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