1. **Stating the problem:** Solve an exponential equation that leads to an algebraic expression. 2. **General approach:** Exponential equations often have the form $a^{f(x)} = b$, where $a$ and $b$ are constants and $f(x)$ is an algebraic expression. To solve, we often take logarithms or rewrite the equation to isolate the algebraic expression. 3. **Example problem:** Solve $2^{x+1} = 8$. 4. **Step 1: Express both sides with the same base if possible.** Since $8 = 2^3$, rewrite the equation as: $$2^{x+1} = 2^3$$ 5. **Step 2: Set the exponents equal.** Because the bases are equal and nonzero, the exponents must be equal: $$x + 1 = 3$$ 6. **Step 3: Solve the algebraic equation.** Subtract 1 from both sides: $$x = 3 - 1 = 2$$ 7. **Answer:** The solution to the equation $2^{x+1} = 8$ is $x = 2$. This method applies generally: rewrite exponential expressions with the same base, then solve the resulting algebraic equation.