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Multiply through by 2: 3-e^x=2e^2x+2. So 2e^2x+e^x-1=0. This factorises: (2e^x-1)(e^x+1)=0, so e^x=-1, which has no real solution, because it would imply getting the log of a negative number, or e^x=0.5, making x=ln(0.5)=-0.6931.
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