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: 76



Work Step by Step

Re-write the given equation as: $(3^2)^{2x} \cdot (3^3)^{x^2}=3^{-1} ...(1)$ We know that $a^{m} \cdot a^n =a^{m+n}$ So, we can write equation (1) as: $3^{4x+3x^2}=3^{-1}$ Use the rule power rule: $a^p=a^q$ . We can see that the base $a=3$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $4x+3x^2=-1 \\ 3x^2+4x+1=0 \\ (3x+1)(x+1)=0$ By the zero-product property, we have: $x=-1,\dfrac{-1}{3}$
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