Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.6 - Exponential and Logarithmic Equations; Further Applications - 9.6 Exercises - Page 630: 42

Answer

$x=\dfrac{3}{2}$

Work Step by Step

Since $\log_b m=\log_b n $ implies $m=n$, then the given equation, $ \log (7-2x)=\log 4 $, implies \begin{align*}\require{cancel} 7-2x&=4 .\end{align*} Using the properties of equality, the equation above is equivalent to \begin{align*}\require{cancel} 7-4&=2x \\ 3&=2x \\\\ \dfrac{3}{2}&=\dfrac{\cancel2x}{\cancel2} \\\\ \dfrac{3}{2}&=x \\\\ x&=\dfrac{3}{2} .\end{align*} Hence, the solution to the equation $ \log (7-2x)=\log 4 $ is $ x=\dfrac{3}{2} $.
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