Convert the logarithmic equation into exponential form. The statement log_5(x + 7) = 2 means x + 7 = 5^2. Now calculate 5^2 = 25, so x + 7 = 25. Subtract 7 from both sides: x = 25 - 7 = 18. Finally, check the domain: x + 7 must be positive, and 18 + 7 = 25 > 0, so the answer is valid.