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: 86

Answer

$x = ±7$

Work Step by Step

$\frac{2.4x^{6}-19}{1000} = 282.3386$ $2.4x^{6} - 19 = 282338.6$ $2.4x^{6} = 282357.6$ $x^{6} = 117,649$ $x = ±(117,649)^{\frac{1}{6}}$ $x = ±7$ Check: When $x= 7$ $\frac{2.4x^{6}-19}{1000} \overset{?}{=} 282.3386$ $\frac{2.4(7)^{6}-19}{1000} \overset{?}{=} 282.3386$ $\frac{2.4(117,649)-19}{1000} \overset{?}{=} 282.3386$ $\frac{282357.6-19}{1000} \overset{?}{=} 282.3386$ $\frac{282338.6}{1000} \overset{?}{=} 282.3386$ $282.3386 = 282.3386$ When $x = -7$ $\frac{2.4x^{6}-19}{1000} \overset{?}{=} 282.3386$ $\frac{2.4(-7)^{6}-19}{1000} \overset{?}{=} 282.3386$ $\frac{2.4(117,649)-19}{1000} \overset{?}{=} 282.3386$ $\frac{282357.6-19}{1000} \overset{?}{=} 282.3386$ $\frac{282338.6}{1000} \overset{?}{=} 282.3386$ $282.3386 = 282.3386$
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