SOLUTION: solve the equation (e^2x)-(e^x)=2 My first instinct to solve this problem was to factor out e^x on the left side but didn't know how to rewrite that... e^x(^2-1)=2 ?? My

Question 889524: solve the equation (e^2x)-(e^x)=2
My first instinct to solve this problem was to factor out e^x on the left side but didn't know how to rewrite that... e^x(^2-1)=2 ??
My second instinct was to set the equation to 0. (e^2x)-(e^x)-2=0, then factor but wasn't sure how to go about that.
Which method should I use and what would the following steps be?
Also, this is a multiple choice question. The answer choices are:
a. 2 only
b. -1 or 2 only
c. ln 2
d. e^-1 or e^2
e. e^2 only
Thank you very much for taking your time to help me.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the equation (e^2x)-(e^x)=2
---------
Use substitution
u = e^x
u^2 - u - 2 = 0
(u-2)*(u+1) = 0
--> u = e^x = -1 (not allowed)
u = e^x = 2
x = ln(2)

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