So regards logging from SO and other sites on the Internet the best response seems to be:
void DoSomething() {
Logger.Log(\"Doing something!\");
// Code.
I've only ever written a few unit tests for logging. It's a pain, either making the production code messy (due to injecting the logger) or the test smelly (replacing the static logger with a mock). Unlike McWafflestix, I've often not found it to be worth the effort afterwards.
How much do you really want to know whether the logging is working, beyond what you'll see through other (hands-on) testing? You might want to use DI for the occasional class where logging is really important, but otherwise I just wouldn't bother testing logging.
This is assuming the log is of a debug nature - if it's an audit log or something like that (something with a functional requirement) that's a different matter.