Solve for x e2x4ex3 e2x4ex3Solutionex2 4e3 3 let ex t t2

Solve for x

e^2x=4e^x-3

e^2x=4e^x+3

Solution

(e^x)^2 = 4e^3 - 3

let e^x = t

t^2 - 4t + 3 =0

(t-3) ( t-1) = 0

t = 3, 1

e^x = 3,1

x log e = 3

x = 3

x = 1

(e^x)^2 = 4e^3 + 3

let e^x = t

t^2 - 4t - 3 =0   

(t - 4.64) (t +0-.64) = 0

t = 4.64 , - 0.64

x = 4.64, -0.64