Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 23

$-2$

Step 1. Rewrite the equation as $log_8[(x+6)(x+4)]=1 \longrightarrow log_8(x^2+10x+24)=1$ Step 2. Thus $x^2+10x+24=8\longrightarrow x^2+10x+16=0\longrightarrow (x+8)(x+2)=0\longrightarrow x=-8,-2$. Step 3. Check answers, only $x=-2$ fits the original equation.