College Algebra (11th Edition)

Published by Pearson

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises - Page 410: 64

Answer

$x=-2$

Work Step by Step

We rewrite both sides, so that the base is $\frac{3}{2}$ on both sides. Left side: $\frac{2}{3}^x$. By the law of exponents:$\frac{1}{a}^x=a^{-x}$ $\frac{2}{3}^x=\frac{3}{2}^{-x}$ Right side: $\frac{9}{4}=\frac{3}{2}^2$ Thus, the given equation is equivalent to: $\frac{3}{2}^{-x}=\frac{3}{2}^2$ Since the bases are the same, we set the exponents equal: $-x=2 \\-1(-x)=-1(2) \\x=-2$

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