Dark Knight vs Old Man Logan

This comes from a (drunk) conversation I had last night. Can a bloodlusted dark knight take out old man Logan? Mutually assured destruction also counts as a win for dark knight since his goal is to wipe out Logan.

Vs

If he can't do it then what happens if the dark knight gets 2 days prep? Would it make any difference?

Fight takes place in Gotham. with prep batman can ambush Logan anywhere within Gotham that might give him the advantage.

I've had this conversation with many of my friends several times. I believe Logan takes this fight if there isn't any prep involved. Bruce was having trouble against the joker when all he had was a stiletto. There's no way he'll beat a blood lusted Logan old or not. With the two days of prep, I think that Bruce can pull out the win. All he has to do is create another of his strength enhancement suits. With two days prep, he'd realize that he just needs to overtax Logan's healing factor.