I can't figure out how to solve: e^x +e^-x = 3.  My teacher gave the answer, but I don't get how he get's there.

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You could do it analytically but that would take a long time and there is really no use.Just do it graphically. In you calculator set y1= e^x+e^-x and y2=3and find your intersect.Its as simple as that..