1. **State the problem:** Solve the logarithmic equation $$\log_3 (x + 5) = 4$$ and find the exact solution(s), rejecting any values not in the domain. 2. **Recall the definition and domain:** The logarithm $$\log_3 (x + 5)$$ is defined only if $$x + 5 > 0$$, so $$x > -5$$. 3. **Rewrite the logarithmic equation in exponential form:** $$\log_3 (x + 5) = 4 \implies x + 5 = 3^4$$ 4. **Calculate the right side:** $$3^4 = 81$$ 5. **Solve for $$x$$:** $$x + 5 = 81 \implies x = 81 - 5 = 76$$ 6. **Check the domain:** Since $$76 > -5$$, the solution is valid. **Final answer:** $$\boxed{76}$$