1. **State the problem:** Solve the equation $$j(x) = e^{2x} - 3e = 2e$$ for values of $x$. 2. **Rewrite the equation:** We want to find $x$ such that $$e^{2x} - 3e = 2e$$ 3. **Isolate the exponential term:** Add $3e$ to both sides: $$e^{2x} = 2e + 3e$$ $$e^{2x} = 5e$$ 4. **Divide both sides by $e$:** $$\frac{e^{2x}}{e} = \frac{5e}{e}$$ $$e^{2x - 1} = 5$$ 5. **Simplify the exponent:** Since $\frac{e^{2x}}{e} = e^{2x - 1}$, we have $$e^{2x - 1} = 5$$ 6. **Take the natural logarithm of both sides:** $$\ln\left(e^{2x - 1}\right) = \ln(5)$$ 7. **Use the logarithm power rule:** $$2x - 1 = \ln(5)$$ 8. **Solve for $x$:** $$2x = \ln(5) + 1$$ $$x = \frac{\ln(5) + 1}{2}$$ **Final answer:** $$x = \frac{\ln(5) + 1}{2}$$