1. **Stating the problem:** Solve an exponential equation that simplifies to a linear equation. 2. **General form:** An exponential equation has the form $$a^{x} = b$$ where $a > 0$ and $a \neq 1$. 3. **Example problem:** Solve $$2^{x} = 8$$. 4. **Step 1: Express the right side as a power of the base:** Since $8 = 2^{3}$, rewrite the equation as $$2^{x} = 2^{3}$$. 5. **Step 2: Use the property of equality of exponents:** If $$a^{m} = a^{n}$$ then $$m = n$$. 6. **Step 3: Set the exponents equal:** $$x = 3$$. 7. **Step 4: Verify the solution:** Substitute $x=3$ back into the original equation: $$2^{3} = 8$$ which is true. **Final answer:** $$x = 3$$.