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: 99

Answer

$x = ±3$

Work Step by Step

1. Power 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 $5x^{6} + 20 = 3x^{6} + 1478$ $5x^{6} - 3x^{6} = 1478 -20$ $2x^{6} = 1458$ $x^{6} = 729$ $x = ±(729)^{\frac{1}{6}}$ $x = ±3$ Check: When $x = 3$ $5(3)^{6} + 20 \overset{?}{=} 3(3)^{6} + 1478$ $5(729) + 20 \overset{?}{=} 3(729) + 1478$ $3645 + 20 \overset{?}{=} 2187 + 1478$ $3665 = 3665$ When $x = -3$ $5(-3)^{6} + 20 \overset{?}{=} 3(-3)^{6} + 1478$ $5(729) + 20 \overset{?}{=} 3(729) + 1478$ $3645 + 20 \overset{?}{=} 2187 + 1478$ $3665 = 3665$
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