SOLUTION: Find the exact solution(s) to the equation {{{e^(2x)-2e^(x)-35=0}}}

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Question 258161: Find the exact solution(s) to the equation e%5E%282x%29-2e%5E%28x%29-35=0
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The original equation was
(i) e%5E%282x%29-2e%5E%28x%29-35=0
Let Y = e^x. then Y^2 = e^(2x). We get
(ii) Y%5E2-2Y-35=0
factoring, we get
(iii) %28Y-7%29%28Y%2B5%29+=+0
solving
Y = 7
OR
Y = -5
substituting e^x for Y, we get
(iv) e%5Ex+=+7
so, x = ln(7)
--
(v) e%5Ex+=+-5
gives no solution. so, we are left with
x = ln(7)