Solve the equation. e^2x - 6e^x + 5 = 0

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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 = 0

=> t^2 - 5t - t + 5 = 0

=> t(t - 5) - 1( t - 5) = 0

=> (t - 1)(t - 5) = 0

=> e^x = 1 and e^x = 5

=> x = 0 and x = ln 5

The solution of the equation is x = 0 and x = ln 5

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