Reply by antmjr

Only 1 1/2” thick board? cannot you hole-saw from one side? (be aware that 3’’ diameter may be a lot: are you sure your power drill is strong enough? Mine is a portable METABO 600W, and frankly it would suffer with such a big hole saw)
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Another method is to use the router with a guide bush; here a recess I made this way (black locust) :

-- Antonio