Convert the logarithmic equation into exponential form. The statement log_3(x + 7) = 3 means x + 7 = 3^3. Now calculate 3^3 = 27, so x + 7 = 27. Subtract 7 from both sides: x = 27 - 7 = 20. Finally, check the domain: x + 7 must be positive, and 20 + 7 = 27 > 0, so the answer is valid.