Hi Mitchell,
Unless specified otherwise, Solve does not restrict the domain of the solution. There are infinitely many solutions in the complex domain for any integer value of C[1].
k -> ConditionalExpression[1/10 (2 I ? C[1] + Log[6/5]), C[1] ? Integers]
If you want to restrict the solution to Reals
Solve[30000 == 25000 E^(k 10), k, Reals]
(* {{k -> 0.0182322}} *)
