Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.6 Solving Exponential Equations and Logarithmic Equations - 12.6 Exercise Set - Page 825: 64

Answer

$x=\displaystyle \frac{17}{4}$

Work Step by Step

First, the solutions must satisfy $\left\{\begin{array}{l} x+7\gt 0\\ x-2\gt 0 \end{array}\right.\quad \Rightarrow x\gt 2\qquad (*)$ in order for the equation to be defined. LHS: Apply$ \displaystyle \quad\log_{a}\frac{M}{N}=\log_{a}M-\log_{a}N$ $\displaystyle \log_{6}[\frac{x+7}{x-2}]=\log_{6}5$ ... apply the principle of logarithmic equality $\displaystyle \frac{x+7}{x-2}=5$ $x+7=5(x-2)$ $x+7=5x-10$ $-4x=-17$ $x=\displaystyle \frac{17}{4}\qquad $... satisfies (*), and is a valid solution.
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