Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set: 26

Answer

$x=\dfrac{2}{35}$

Work Step by Step

$\log_{6}(x+2)-\log_{6}x=2$ Combine $\log_{6}(x+2)-\log_{6}x$ as the $\log$ of a division: $\log_{6}\dfrac{x+2}{x}=2$ Rewrite in exponential form: $6^{2}=\dfrac{x+2}{x}$ $\dfrac{x+2}{x}=36$ Take $x$ to multiply the right side of the equation: $x+2=36x$ Solve for $x$: $x-36x=-2$ $-35x=-2$ $x=\dfrac{-2}{-35}$ $x=\dfrac{2}{35}$
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