e^2x-1=e^4 using one to one property?

Do you mean

e^2x - 1 = e^4 or
e^(2x-1) = e^4.
I will assume the 2nd Eq.
(2x-1)*Ln e = 4*Ln e
(2x-1)*1 = 4*1
2x-1 = 4
2x = 5
X = 5/2 = 2.5