1. **State the problem:** Solve the equation $$2^{x+1} + 2^x = 3$$ for $x$. 2. **Recall the properties of exponents:** - $a^{m+n} = a^m \cdot a^n$ - We can factor expressions with common bases. 3. **Rewrite the equation:** $$2^{x+1} + 2^x = 2^x \cdot 2^1 + 2^x = 2 \cdot 2^x + 2^x = 3$$ 4. **Factor out $2^x$:** $$2^x (2 + 1) = 3$$ $$2^x \cdot 3 = 3$$ 5. **Divide both sides by 3:** $$2^x = 1$$ 6. **Solve for $x$:** Since $2^x = 1$, and $2^0 = 1$, it follows that $$x = 0$$ **Final answer:** $$x = 0$$