How do I determine if my kitchen drain pipe is frozen under the slab or outside to the septic tank.?

I know it's not under the sink. Any tips on thawing it out?
It's froze solid. I wouldn't suspect out side going to the septic but my next door neighbors have exactly the same problem on the same day with seperate septics. Same property, around a small lake.

Being where you are, a pro will cost you a small fortune to show up. Home remedy. Open the service cap on the outgoing line and insert a snake to measure out how far the problem is. Get yourself a drill pump and shove a hose as far as you can down the pipe and start pumping. When the pump is doing that, shove a garden hose down to the plug ( the distance estimated by the snake will tell you how far) and turn on the hot water. Fill the pipe and stop the water and drill. Let stand for 5 min and repeat until the pipe opens. Shouldn't take more than 4 or 5 cycles. Once cleared, Insert a long length of roof line heating wire through the pipe to the tank. Don't use pipe heater wire because it is not recommended to be submersed in water, the roof wire is. Drill a small hole in the inspection cover and pass the wire through, sealing it with a little silicone sealer and reinstall. When extreme cold occurs, plug in the heater to keep it from freezing.

After following MA's advise then either rent or have a plumber with a steamer come in and steam the line out. Rooter-Router can do this job.

It's probably not frozen under the slab. Most building codes require the foundation of the building to be below the frost line, i.e. where it won't freeze. This is to prevent the expansion and contraction of ice-encrusted earth from damaging the foundation. If there's a pipe down there, chances are, it won't freeze either. Also, your house is heated, and chances are, your septic tank isn't. If you find where it's frozen (I believe you can get a pipe thermometer) I'd use a hair dryer. It worked on my pipes last week.

Easiest way would be to borrow or buy at your local home center a 50 foot drain snake..(ten bucks or less) run it down the pipe till it hits the blockage and mark it. bring it up and measure the distance that should tell you how far out it is.