Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set: 27

Answer

$x=-1$ and $x=4$

Work Step by Step

$\log_{4}(x^{2}-3x)=1$ Rewrite in exponential form: $4^{1}=x^{2}-3x$ $x^{2}-3x=4$ Take the $4$ to the left side of the equation: $x^{2}-3x-4=0$ Solve this equation by factoring: $(x+1)(x-4)=0$ Set each factor equal to $0$ and solve each individual equation for $x$: $x+1=0$ $x=-1$ $x-4=0$ $x=4$ The initial equation is not undefined for either of the solutions found. Our answer is $x=-1$ and $x=4$
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