1. **State the problem:** Solve the equation $4^{x - 3} = 256$ for $x$. 2. **Recall the formula and rules:** We know that $4^{x - 3}$ means $4$ raised to the power of $(x - 3)$. To solve for $x$, we want to express both sides with the same base if possible. 3. **Express 256 as a power of 4:** Since $4^1 = 4$, $4^2 = 16$, $4^3 = 64$, and $4^4 = 256$, we can write: $$4^{x - 3} = 4^4$$ 4. **Set the exponents equal:** Because the bases are the same and nonzero, the exponents must be equal: $$x - 3 = 4$$ 5. **Solve for $x$:** $$x = 4 + 3$$ $$x = 7$$ **Final answer:** $x = 7$