Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - Review Exercises - Page 414: 96


$x=0.449$ $x=-4.449$

Work Step by Step

$\log_6(x+2)-\log_6x=\log_6(x+5)$ $\log_6(\frac{x+2}{x})=\log_6(x+5)$ Using the one-to-one property: $\frac{x+2}{x}=x+5$ $x+2=x^2+5x$ $0=x^2+4x-2~~$ ($a=1,b=4,c=-2$): $x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-4±\sqrt {4^2-4(1)(-2)}}{2(1)}=\frac{-4±\sqrt {24}}{2}=\frac{-4±2\sqrt 6}{2}=-2±\sqrt 6$ $x=-2+\sqrt 6=0.449$ or $x=-2-\sqrt 6=-4.449$
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