I inherited some 24p 3750's for our infrastructure running IOS 12.1(19). I have 2 48 Port WS-C3750X-48P switches running IOS ipbase9k-mz122-55SE3. The 24's wont stack with the 48's so I updated the IOS images on the 24's to the same IOS as the 48P. I was able to run them all now in the stack but does this need to be licensed?
The older 3750s don't need license, but most new series (3750x, 3850, etc..) need license.
Your 3750x comes with IP Base license. If that is good enough for you, than no further license needed.
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To clarify a bit what Reza noted, all 3750 need licenses, however the original series feature licenses were "paper", the device's IOS doesn't enforce the feature license like the later "E" and "-X" 3750 series do.
Also, to legally upgrade the IOS version (same IOS feature set), I believe you need either a license for the new version or a support contract for the device.