Question

Solve the equation and check the solution(s).
e^2x-2e^x-3=0

Answer 1

let's assume that e^x = y, so it like quadratic :
y^2 - 2y - 3 = 0
factor out then solve for y, first

Answer 2

y=-1, y=3

Answer 3

yes, that's right. now you have to resubtitute them to e^x = y. get
e^x = -1 or e^x = 3
then solve for x

Answer 4

Since e^x can never be negative for any real value of x, you can discard e^x = -1.

Solve e^x = 3.
Take natural logarithm on both sides to solve for x.