(* Definition of log R+* -> R *)
(* Extension on R *)
Definition ln (x:R) : R :=
match Rlt_dec 0 x with
| left a => Rln (mkposreal x a)
| right a => 0
end.
Definition Rlog x y := (ln y)/(ln x).

Theorem ln_mult : forall x y:R, 0 < x -> 0 < y -> ln (x * y) = ln x + ln y.