1. **State the problem:** Solve the equation $$\ln(x - 8) + \ln 3 = 3$$ given the square root values 4 and 25 (which might be hints for simplification). 2. **Recall the logarithm property:** The sum of logarithms with the same base can be combined as the logarithm of the product: $$\ln a + \ln b = \ln(ab)$$ 3. **Apply the property:** $$\ln(x - 8) + \ln 3 = \ln(3(x - 8))$$ So the equation becomes: $$\ln(3(x - 8)) = 3$$ 4. **Rewrite the equation in exponential form:** Since $$\ln y = 3$$ means $$y = e^3$$, we have: $$3(x - 8) = e^3$$ 5. **Solve for $$x$$:** $$x - 8 = \frac{e^3}{3}$$ $$x = 8 + \frac{e^3}{3}$$ 6. **Check domain restrictions:** The argument of the logarithm must be positive: $$x - 8 > 0 \implies x > 8$$ Our solution satisfies this. 7. **Final answer:** $$\boxed{x = 8 + \frac{e^3}{3}}$$