1. **State the problem:** Solve the equation $$4^x + 4^x = 128$$ for $x$. 2. **Combine like terms:** Since both terms are $4^x$, we can write: $$4^x + 4^x = 2 \times 4^x$$ 3. **Rewrite the equation:** $$2 \times 4^x = 128$$ 4. **Isolate $4^x$:** $$4^x = \frac{128}{2} = 64$$ 5. **Express 64 as a power of 4:** Since $4^3 = 64$, we have: $$4^x = 4^3$$ 6. **Set exponents equal:** Because the bases are the same and the function is one-to-one, $$x = 3$$ **Final answer:** $$x = 3$$