Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 31

$\frac{9}{2}=4.5$

Step 1. Rewrite the equation as $log_{a}[(x-1)(x+3)]=log_{a}[(x-2)(x+6)] \longrightarrow log_{a}(x^2+2x-3)=log_{a}(x^2+4x-12)$ Step 2. Thus $x^2+2x-3=x^2+4x-12\longrightarrow 2x=9\longrightarrow x=\frac{9}{2}=4.5$. Step 3. Check answers, $x=\frac{9}{2}=4.5$ fits the original equation.