L&E, 2ADV E1 2025 MET1 5 Solve \(e^{2 x}-8 e^x+7=0\) for \(x\). (3 marks) --- 8 WORK AREA LINES (style=lined) --- Show Answers Only \(x=\ln 7, \ x=0\) Show Worked Solution \(\text{Solve}\ \ e^{2 x}-8 e^x+7=0:\) \(\text{Let} \ \ X=e^x\) \(X^2-8 X+7\) \(=0\) \((X-7)(X-1)\) \(=0\) \(x=7 \ \text{or 1}\) \(e^x=7 \ \ \qquad e^x=1\) \(x=\ln 7 \qquad x=0\)