To the best of my knowledge (I use this same model router, but I've updated it with the DD-WRT firmware), the log on a router is relatively small (there isn't a lot of storage on such a device). However, if you can log on to the router using your browser (point it to the "gateway address" in your IP settings) you should be able to see the management options. Of course, you will have to use your administrator userid and password to gain access to the configuration page.
Are you sure you want to delete the router logs? Perhaps you're more concerned with the actual tracking data left on your computer? Most of the Internet connection information is stored on the client computer and not the router. Check your Internet settings and delete cookies and favorites as well as your browser history.
There are commercial products available, and some freeware ones (such as CCleaner) that will automate and ease this process for you.