Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 32

$4$

Step 1. Rewrite the equation as $log_{a}[(x)(x-2)]=log_{a}(x+4) \longrightarrow log_{a}(x^2-2x)=log_{a}(x+4)$ Step 2. Thus $x^2-2x=x+4\longrightarrow x^2-3x-4=0\longrightarrow (x+1)(x-4)=0 \longrightarrow x=-1,4$. Step 3. Check answers, $x=4$ fits the original equation.