1. **State the problem:** Solve the equation $$3^x = 27$$. 2. **Recall the formula and rules:** We know that 27 can be expressed as a power of 3 because $$27 = 3^3$$. 3. **Rewrite the equation:** Replace 27 with $$3^3$$ to get $$3^x = 3^3$$. 4. **Apply the rule of equality of exponents:** If $$a^m = a^n$$ and $$a > 0$$, then $$m = n$$. 5. **Set the exponents equal:** $$x = 3$$. 6. **Final answer:** $$x = 3$$. This means the value of $$x$$ that satisfies the equation $$3^x = 27$$ is 3.