Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises: 53

Answer

$x_{1}=4;x_{2}=-6$

Work Step by Step

$\log _{3}\left[ \left( x+5\right) \left( x-3\right) \right] =2\Rightarrow \left( x+5\right) \left( x-3\right) =3^{2}$ $ \Rightarrow x^{2}+2x-15=9\Rightarrow x^{2}+2x-24=0$ $\Rightarrow x^{2}+2x+1-25=0\Rightarrow \left( x+1\right) ^{2}-5^{2}=0\Rightarrow \left( x+1-5\right) \left( x+1+5\right) =0$ $\Rightarrow \left( x-4\right) \left( x+6\right) =0\Rightarrow x_{1}=4;x_{2}=-6$
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