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: 43



Work Step by Step

Using the rules of logarithms to solve the equation, we find: $$\log _3\left(\left(x-9\right)\left(x-3\right)\right)=2 \\ \log _3\left(\left(x-9\right)\left(x-3\right)\right)=\log _3\left(9\right) \\ x=3\left(2+\sqrt{2}\right),\:x=3\left(2-\sqrt{2}\right)$$ Checking for extraneous solutions, we see that only $x=3\left(2+\sqrt{2}\right)$ is valid.
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