Paul, you will see opinions on this subject that range from being okay with a carpenter's level to guys who say that you should get a master precision level. All of us are faced with the exact question you're asking so I'll offer an opinion.
A lathe is leveled not just once or twice or three times. Over it's lifetime, a lathe will need to be re-leveled many times so I feel having a good level that will get you very close is a worthwhile investment. The level does not need to be super-expensive but it should be sensitive. By that, I mean it should read to 0.0002-0.0005" over a 10-12" span. The reason for this degree of sensitivity is that it saves you time. Once the lathe is level with one of these contraptions it usually only takes a slight tweak after doing a 2-collar test and you're done. Less sensitive levels will require more work to get you to that point.
A level of this type need not be expensive if an import is okay. You will find them in a 10-12" length for under $100.00 on ebay, like this one:
http://www.ebay.com/itm/8-Precision...hash=item258b5edad4:m:m9eGS-so0O0PoDsPDcLo7Bg
Mine is a Kinex, an 11.5" long level sensitive to 0.02mm/M, or 0.0002"/10"; this is the same sensitivity as the one I linked to above but that one can be had for far less than mine cost.
You may stay with your 10" Logan but you may switch someday and the level will be there for you. I suggest a 10-12" long level so you can use it on any lathe you buy/have. Once you have one, learn to calibrate it and use it correctly.
Hope that helps.