Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - 7.6 Exercises - Skill Practice - Page 520: 41



Work Step by Step

Using the rules of logarithms to solve the equation, we find: $$\log _5\left(\left(x+4\right)\left(x+1\right)\right)=2 \\ \log _5\left(\left(x+4\right)\left(x+1\right)\right)=\log _5\left(25\right)\\ \left(x+4\right)\left(x+1\right)=25 \\ x=\frac{-5+\sqrt{109}}{2},\:x=\frac{-5-\sqrt{109}}{2}$$ Checking for extraneous solutions, we see that only $x=\frac{-5+\sqrt{109}}{2}$ is valid.
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