[Haskell-cafe] Help with another Bird problem (3.3.4)

Could someone provide a solution to do the following problem from Bird: The function "log" can be specified by the condition that log (2^m) = m for all m. Construct a program for log and prove that it meets the specification. Note that this problem doesn't specify a domain, unlike problem 3.3.3, which specified Nat as the domain. Thanks.