The good news is that you can integrate your work with the Rust Log library. Basically the difference is: instead of using your logging functions, the user will use the logging macros provided by Log. This means that they can log to the terminal using your library, to a disk file, and to a remote service. All at the same time using the same logging macros.
Here is the Rust Log library description:
> Libraries should link only to the log crate, and use the provided macros to log whatever information will be useful to downstream consumers.