Math Problem Solver

The solution is: $$x = \frac{4 + e^{4}}{e^{2}} \approx 7.9303972$$

$$\begin{aligned}{e}^{2} x - {e}^{4} &= {e}^{x} + 1 - {e}^{x} + 3\\x e^{2} - e^{4} &= 4\\x e^{2} &= 4 + e^{4}\\x &= \frac{4 + e^{4}}{e^{2}}\end{aligned}$$

$e$ is Euler's number, a mathematical constant that is approximately $2.71828$.