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: 57

Answer

$x = 4$

Work Step by Step

$7(2)^{x} = 48 + 4(2)^{x} $ $7(2)^{x} - 4(2)^{x} = 48$ $(7-4)((2)^{x} ) = 48$ $3(2)^{x} = 48$ $(2)^{x} = 16$ $(2)^{x} = (2)^{4} $ $x = 4$ Check $7(2)^{4} \overset{?}{=} 48 + 4(2)^{4} $ $7(16) \overset{?}{=} 48 + 4(16)$ $112 \overset{?}{=} 48 + 64$ $112 = 112$
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