Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 21

$-6$

Step 1. Rewrite the equation as $log_2[(x+7)(x+8)]=1 \longrightarrow log_2(x^2+15x+56)=1$ Step 2. Thus $x^2+15x+56=2\longrightarrow x^2+15x+54=0\longrightarrow (x+9)(x+6)=0\longrightarrow x=-9,-6$. Step 3. Check answers, only $x=-6$ fits the original equation.