College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4 - Page 490: 71



Work Step by Step

Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable. Then simplify the side with $x$ by factoring and then solving for $x$. $-3$ is not part of the domain, so $6$ is the only answer. $\log_2(x+2)-\log_2(x-5)=3$ $\log_2(x+2)(x-5)=3$ $8=x^2-3x-10$ $x^2-3x-18=0$ $(x+3)(x-6)=0$ $x=-3, x=6$ $x=6$
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