1. **State the problem:** Solve the equation $$\frac{2e^x}{2} - 3 = e^9$$ for $x$. 2. **Rewrite the equation:** Simplify the left side by canceling the 2 in numerator and denominator: $$\frac{\cancel{2}e^x}{\cancel{2}} - 3 = e^9$$ which simplifies to $$e^x - 3 = e^9$$ 3. **Isolate the exponential term:** Add 3 to both sides: $$e^x = e^9 + 3$$ 4. **Solve for $x$:** Take the natural logarithm (ln) of both sides: $$x = \ln\left(e^9 + 3\right)$$ 5. **Final answer:** $$x = \ln\left(e^9 + 3\right)$$ This is the exact solution. Since $e^9$ is a large number, $x$ is slightly larger than 9.