Question

How do you solve `e^(2x) = 2e^x + 1 = 0`?

Answer 1

See explanation.

Explanation:

If you substitute the expression `e^x` with a new variable you get a quadratic equation:

`e^(2x)-2e^x+1=0`

`t^2-2t+1=0`

`(t-1)^2=0`

`t=1`

Now we have to return to `x` by solving:

`e^x=1=>e^x=e^0=>x=0`

Answer: The equation has one solution `x=0`.