Intermediate Algebra: Connecting Concepts through Application

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

Chapter 6 - Logarithmic Functions - 6.5 Solving Exponential Equations - 6.5 Exercises: 44

Answer

$x = 1, 2 $

Work Step by Step

$(\frac{1}{4})^{x^{2} - 3x} = 16$ $(4^{-1})^{x^{2} - 3x} = 4^{2}$ $4^{-x^{2} + 3x} = 4^{2}$ $-x^{2} + 3x = 2$ $-x^{2} + 3x - 2 = 0$ $-x^{2} + 2x + x - 2 = 0$ $-x(x - 2) + 1(x-2) = 0$ $(-x + 1)(x-2) = 0$ $-x + 1 = 0$ $-x = -1$ $x = 1$ $x -2 = 0$ $x = 2$ $x = 1, 2 $
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