Weight a foundation can hold
Log homes are designed to distribute the weight of the house fairly evenly around the perimeter and with the logs being about 16” wide it could easily support about 3,500 lbs. per linear foot, depending on soil conditions in your area. 

However, the reason footings (or as @isherwood indicated, thickened slabs at edges) are used is 1) to be installed below frost lines, which could be from 12” down to 48” below ground level, depending where you live, 2) help span across soft spots in the soil, and 3) removes loose topsoil which is easily compressed. Your slab does not do any of those. 

In addition, if you have any posts in the middle of your house, that is a “concentrated “ load and will require an extra large footing with extra reinforcement.  A 6” slab will fail, even with rebar installed, as you indicated.