Given : ln(x) = 1/x; Chain Rule; x = 1. Solve:
(1) ln(e^x) = x = 1
ln(e^x) = ln(u) e^x (Set u=e^x)
= 1/u e^x = 1/e^x e^x = 1 (equation 1)
e^x = e^x   Q.E.D.