Question - Logarithmic Equation Problem

\text{已知等式：}\log_3(x + 4) + \log_3(x - 2) = 3.

\text{应用对数法则合并同底对数：}\log_3[(x + 4)(x - 2)] = 3.

\text{化简等式得：}\log_3(x^2 + 2x - 8) = 3.

\text{消去对数得：}x^2 + 2x - 8 = 3^3.

\text{解方程：}x^2 + 2x - 8 = 27.

x^2 + 2x - 35 = 0.

(x + 7)(x - 5) = 0.

\text{所以解为：}x = -7 \text{ 或 } x = 5.