SOLUTION: solve the exponential equation. e^2x + e^x -6=0

Question 240209: solve the exponential equation.
e^2x + e^x -6=0
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
e^2x + e^x -6=0
.
This is simply a "quadratic equation":
.
Let y = e^x
then
y^2 = (e^x)^2 = (e^x)(e^x) = e^2x
.
So now we can rewrite:
e^2x + e^x -6=0
y^2 + y -6=0
(y+3)(y-2) = 0
y = {-3, 2}
.
Since we said:
y = e^x
ln y = x
.
So,
x = ln 2 (this is your solution)

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