log of search terms

Is there an easy way to log search terms from users? Specifically, I mean when forum members type into any search box from any page. It would be useful over time to analyze the terms so that we can better understand site usage.
The vanilla db has Activity and ActivityType tables that would seem to be the appropriate place to log this data but there is no indication that search terms are stored.
The vanilla db has Activity and ActivityType tables that would seem to be the appropriate place to log this data but there is no indication that search terms are stored.
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