It is probably leaking form the drain flange. I just fixed the same thing at my bro-in-laws rental.
You can't caulk it.
You need to remove disposal...pull up pants so ass-crack is not showing.
Remove flange nut under sink (attached to bottom of "drain" -- the big silver thing in the sink)
Pull out drain flange.
Clean off all old cracked putty.
Get plumbers putty and roll into joint sized peices in a circle around "hole"
Apply to SINK about 1/4" from "hole" in sink.
Put drain flange back in and push down. Putty will ooze out.
Reinstall flange nut and tighten (use a big ass screwdriver, etc. to hold drain flange so it doesn's spin).
Should take you no more than 30 minutes, even being a noob to it.
I've done this about 10 times at various houses/rentals. If in doubt, just go to the hardware store and inquire....they will be able to tell you how to fix it. Just look for an old-timer.
Hope this helps....
There is no "easy fix". You need to do it right.
Tim (apparently likes "3" cars)
E90 M3 -- Current ride
2004 GT3 -- Sold
1997 M3/4 -- Sold
1995 M3 -- Sold