There are a few ways you can approach this:
1.) Your Apache logs should show you how many searches are being performed from the outside. Using pattern matching, you can probably generate reports from them relatively easily.
2.) Your Jetty logs (found in solr/jetty/logs) should give you information about how much Solr is being accessed (i.e. it records the communication between VuFind and Solr). There’s a lot of noise in these logs because VuFind frequently pings Solr, and you’d have to do some work to distinguish between record views and searches, but again, with a bit of filtering, you could probably generate reports programmatically from this data.
3.) VuFind includes an optional statistics component which records activity data to a special Solr core – you can turn this on in config.ini. That won’t help you with past data, but it might be useful in the future. However, be aware that the current reporting functionality is very limited, and I’ve heard of performance issues related to statistics in heavily used systems. The statistics feature is completely rewritten in the forthcoming VuFind 2.0, so it might not be worth getting too attached to its 1.x form.
I hope this is helpful – let me know if you have questions. Also, if you succeed in generating reports using approach 1 or 2, please consider sharing your work; I’m sure others might be interested in doing similar things.