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: 19

Answer

$x=\dfrac{3}{4}$

Work Step by Step

$\log_{2}6-\log_{2}x=3$ Combine $\log_{2}6-\log_{2}x$ as the $\log$ of a division: $\log_{2}\dfrac{6}{x}=3$ Rewrite this equation in exponential form: $2^{3}=\dfrac{6}{x}$ $\dfrac{6}{x}=8$ Solve for $x$: $\dfrac{x}{6}=\dfrac{1}{8}$ $x=\dfrac{6}{8}$ $x=\dfrac{3}{4}$
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