SOLUTION: Find all the solutions of the equation: 2e^(2x) - 3e^(x) +1 = 0

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Question 1038416: Find all the solutions of the equation: 2e^(2x) - 3e^(x) +1 = 0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=e%5Ex
Then,
u%5E2=e%282x%29
So,
2u%5E2-3u%2B1=0
%28u-1%29%282u-1%29=0
Two solutions:
u-1=0
u=1
e%5Ex=1
x=0
and
2u-1=0
2u=1
u=1%2F2
e%5Ex=1%2F2
x=ln%281%2F2%29