Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 5 - Exponential Functions - 5.2 Solving Equations Using Exponent Rules - 5.2 Exercises: 102

Answer

1. Exponential equation 2. $x = -4$

Work Step by Step

1. Exponential equation For example: $7^{x} + 3 = 0$ is an exponential equation. (The variable is the exponent.) $x^{7} + 3 =0 $ is a power equation. (The variable is raised to the power of a number.) 2. Solve $7(\frac{1}{3})^{x} + 142 = 2(\frac{1}{3})^{x} + 547$ $7(\frac{1}{3})^{x} - 2(\frac{1}{3})^{x} = 547 - 142$ $(7-2)(\frac{1}{3})^{x} = 405$ $5(\frac{1}{3})^{x} = 405$ $(\frac{1}{3})^{x} = 81$ $3^{-x} = 81$ $3^{-x} = 3^{4}$ $-x = 4$ $x = -4$ Check: $7(\frac{1}{3})^{-4} + 142 \overset{?}{=} 2(\frac{1}{3})^{-4} + 547$ $7(81) + 142 \overset{?}{=} 2(81) + 547$ $567 + 142 \overset{?}{=} 162 + 547$ $709 = 709$
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