1. **State the problem:** Solve the logarithmic equation $$\log_3(3x - 11) = \log_3(25 - x)$$ and check for extraneous solutions. 2. **Recall the logarithm property:** If $$\log_b A = \log_b B$$, then $$A = B$$, provided $$A > 0$$ and $$B > 0$$. 3. **Apply the property:** Set the arguments equal: $$3x - 11 = 25 - x$$ 4. **Solve for $$x$$:** $$3x - 11 = 25 - x$$ Add $$x$$ to both sides: $$3x + x - 11 = 25$$ $$4x - 11 = 25$$ Add 11 to both sides: $$4x = 36$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{36}{4}$$ $$x = 9$$ 5. **Check for extraneous solutions:** Check the arguments of the logarithms for $$x=9$$: $$3(9) - 11 = 27 - 11 = 16 > 0$$ $$25 - 9 = 16 > 0$$ Both arguments are positive, so $$x=9$$ is valid. **Final answer:** $$x = 9$$