1. **State the problem:** Solve the inequality $$3^x < 9^{x - 2}$$. 2. **Express both sides with the same base:** Since $$9 = 3^2$$, rewrite the right side as $$9^{x-2} = (3^2)^{x-2} = 3^{2(x-2)}$$. 3. **Rewrite the inequality:** $$3^x < 3^{2(x-2)}$$. 4. **Use property of exponential inequality:** Since the base $$3 > 1$$, the inequality direction stays the same. So, compare the exponents: $$x < 2(x-2)$$. 5. **Solve the inequality for $$x$$:** $$x < 2x - 4$$ Subtract $$2x$$ from both sides: $$x - 2x < -4$$ $$-x < -4$$ Multiply both sides by $$-1$$ (reversing inequality direction): $$x > 4$$. 6. **Final answer:** $$x > 4$$ satisfies the inequality.