Solve for x: e^x - e^(-x) = 2

Answer 1

Try writing like this:

e^x - 1/e^x= 2

Multiply through by e^x_{, resulting in}

e^2x - 1 = 2e^x

e^2x - 2e^x - 1 = 0

This is quadratic in e^x.

Use the quadratic formula where a = 1, b = -2, c = -1 to solve for e^x. The negative root will be rejected since there is no exponent applied to base e that will generate a negative value.

Once you have e^x = "the positive root from the quadratic formula", take ln of both sides to isolate x.

Try graphing f(x) = e^x - e^-x and y = 2 on the Desmos online graphing calculator, locate the point of intersection to confirm your result.