Your logs should always include IP addresses (in addition to hostnames)
Although I was grumpy about Exim's logging yesterday, there is one thing it gets absolutely right: it always logs the IP address as well as the hostname. The importance of this goes well beyond doing reverse lookups right; even if your program is fully validating the hostname, you should log the IP address as well. In fact, my view is that either the IP address or the (verified) hostname alone is incomplete information and you should always log both. Why is quite simple:
What IP address a hostname resolves to can change over time.
Yes, right now logging just the hostname lets me determine the IP address your program saw. But that doesn't necessarily help if I'm going back to the logs a day, a week, a month, or six months later, because then I can't be sure that the IP address I'm resolving today is the same IP address that I would have looked up immediately after your program logged its message. For that matter, the hostname may have stopped resolving entirely by the time I look it up.
(In some cases hostnames can change their IP addresses much faster, including 'right after you verified the IP address'.)
The same is true of logging the IP address alone; by the time I go to look up the hostname it may have changed (especially if I'm doing this well after the fact). Logging the hostname too is especially important if your program made access decisions or whatever based on the hostname instead of the IP address, because then I really want to know what your program was using as the basis for its decision. However, if your program doesn't normally look up the hostname at all it's okay to just log the IP address; there's no need to go to extra work and extra time just to satisfy my moderate curiosity.
(Technically even the hostname and the IP address isn't really sufficient information to reconstruct 'who the IP address belonged to' at a later date; you also need to know things like which ASN it belonged to at the time and its routing and so on. But that is way more than is required in anything but the most cautious organizations. And if you care about this stuff, there are cautions.)