1. **State the problem:** Solve the equation $$4^{x+1} + 4^x = 320$$ for $x$. 2. **Recall the properties of exponents:** We know that $$4^{x+1} = 4^x \cdot 4^1 = 4 \cdot 4^x$$. 3. **Rewrite the equation using this property:** $$4 \cdot 4^x + 4^x = 320$$ 4. **Factor out the common term $4^x$:** $$4^x (4 + 1) = 320$$ $$4^x \cdot 5 = 320$$ 5. **Divide both sides by 5:** $$\cancel{5} \cdot 4^x = \frac{320}{\cancel{5}}$$ $$4^x = 64$$ 6. **Express 64 as a power of 4:** Since $$64 = 4^3$$, we have $$4^x = 4^3$$ 7. **Set the exponents equal (because the bases are the same and nonzero):** $$x = 3$$ **Final answer:** $$x = 3$$