1. **Stating the problem:** Find the value of $x$ that satisfies the equation $$3^{2 - x} = 27.$$ 2. **Recall the formula and rules:** Since $27$ is a power of $3$, rewrite $27$ as $3^3$. The equation becomes: $$3^{2 - x} = 3^3.$$ When the bases are the same and nonzero, the exponents must be equal: $$2 - x = 3.$$ 3. **Solve for $x$:** Subtract 2 from both sides: $$-x = 3 - 2$$ $$-x = 1$$ Multiply both sides by $-1$: $$x = -1.$$ 4. **Conclusion:** The value of $x$ that satisfies the equation is $\boxed{-1}$.