Solve the equation. e^2x - 6e^x + 5 = 0
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justaguide
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We have to solve: e^2x - 6e^x + 5 = 0
e^2x - 6e^x + 5 = 0
let e^x = t
=> t^2 - 6t + 5...
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giorgiana1976 | Student
We'll apply substitution technique to solve the exponential equation.
e^x = t
We'll raise to square both sides:
e^2x = t^2
t^2 - 6t + 5 = 0
We'll apply quadratic formula:
t1 = [6+sqrt(36 - 20)]/2
t1 = (6 + 4)/2
t1 = 5
t2 = 1
But e^x = t1 => e^x = 5
We'll take natural logarithms both sides:
ln e^x = ln 5
x*ln e = ln 5
x = ln 5
e^x = t2=> e^x = 1
x = 0
The solutions of the equation are: {0 ; ln 5}.
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