Convert the logarithmic equation into exponential form. The statement log_4(x + 1) = 3 means x + 1 = 4^3. Now calculate 4^3 = 64, so x + 1 = 64. Subtract 1 from both sides: x = 64 - 1 = 63. Finally, check the domain: x + 1 must be positive, and 63 + 1 = 64 > 0, so the answer is valid.