Determining the exit page for a site is difficult to do reliably (without custom code in your site -- I'll get to that). For example, let's say I open serverfault.com and begin researching the answer to a question. That research takes me down the proverbial rabbit hole, and I don't actually get back to my serverfault browser window for 30 minutes.
From web logs alone, you can't determine whether my 30 minute absence was an "exit" followed by a new visit, or a "pause" of an existing visit. And that's just one example out of many of why a user might become "idle" on a site without it being a real "exit".
That's why analysis tools like Web Log Expert rely on a visitor timeout. You have to make your own assessment of how long a user would have to be idle to be considered having exited the site.
Of course, your log analysis tool (I'm generalizing here, because there are a lot of options out there) needs a way of differentiating users. IP address and User Agent string are not sufficient. For example, there may be multiple users in an office or school somewhere, all of them using homogenized OSes and browsers and coming in through a proxy or NAT (your server would see them all as the same IP and same UA string).
In IIS (not knowing which version, so I'll be vague) open the field selection dialog in the logging config. If Cookie is not checked off, check it (this is assuming that your site uses a session cookie). Also check off Referer.
These two options may make your log files a lot larger, but will give your analysis tool the ability to differentiate users (by session cookie), as well as their path through the site (by referer). AFAIK those fields are not enabled by default.
If you really want an accurate representation of when a user exits your site (closes browser or navigates elsewhere), you can implement an AJAX call on a timer in each of your pages that calls to a URL every X seconds. You can then set the visitor timeout in your analysis tool to something like X+2 seconds. Then you'll know exit times to an accuracy of X+2 seconds. Of course, exit pages will often be reported as being the URL of the AJAX call, so you'd need to somehow have the analysis tool ignore those as exit pages, but not ignore them when checking the visitor timeout.
Whether that's possible would depend upon the tool. I have no experience with Web Log Expert, so I couldn't say for certain.
There's always been a lot of debate as to which log analyzer is the best. IMO you need to try a bunch of them and find the one that best fits the balance of your needs for ease of use, complexity (or simplicity) of reports, speed, and presentation.