Chapter 5 - Exponential and Logarithmic Functions - 5.6 Logarithmic and Exponential Equations - 5.6 Assess Your Understanding - Page 311: 30

$67$

Step 1. Rewrite the equation as $log_{4}(x^2-9)=log_{4}(x+3)+3 \longrightarrow log_{4}(x^2-9)=log_{4}(x+3)+log_464$ Step 2. Thus $x^2-9=64x+192\longrightarrow x^2-64x-201=0\longrightarrow (x+3)(x-67)=0\longrightarrow x=-3,67$. Step 3. Check answers, only $x=67$ fits the original equation.