Answer
$\pm\sqrt 3$
Work Step by Step
1. $2log_{13}(x+2)=log_{13}(4x+7) \Longrightarrow log_{13}(x+2)^2=log_{13}(4x+7) \Longrightarrow (x+2)^2=4x+7 \Longrightarrow x^2+4x+4=4x+7 \Longrightarrow x=\pm\sqrt 3$.
2. Check $x=\pm\sqrt 3$ fit(s).
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 37
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