Strategy: (1) Combine logs using product/quotient rules. (2) Convert to exponential form. (3) Solve the resulting algebraic equation. (4) CHECK all solutions against the original domain (all arguments > 0, all bases > 0 and != 1). Step 4 is non-negotiable — it eliminates extraneous solutions. Example: log(x) + log(x-3) = 1 gives $x^{2-3x}$ = 10, x = 5 or x = -2. Domain requires x > 0 AND x-3 > 0, so x > 3. Only x = 5 is valid.