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

[Peter Hilal]

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.