1. **State the problem:** Solve the equation $1 - 2^{3-x} = 0$ for $x$. 2. **Isolate the exponential term:** Add $2^{3-x}$ to both sides and subtract 0 from both sides: $$1 = 2^{3-x}$$ 3. **Rewrite the equation:** We want to solve for $x$ in the equation: $$2^{3-x} = 1$$ 4. **Recall an important rule:** Any number (except 0) raised to the power 0 equals 1, i.e., $$a^0 = 1$$ 5. **Set the exponent equal to zero:** Since $2^{3-x} = 1$, then $$3 - x = 0$$ 6. **Solve for $x$:** $$x = 3$$ 7. **Final answer:** $$\boxed{3}$$