Help with natural log math problem

Solve for x:

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

e^(x+2) = (e^x) + 2
(e^x)*e^2 = (e^x)+2
(e^x) (e^2 -1) = 2
e^x = 2/(e^2 -1)

x= ln[2/(e^2 -1)] = ln2 - ln(e^2-1)= ln2 - ln(e-1) - ln(e+1) = -1.16143936....