Cut two 2-by-4-foot pieces from a sheet of 1-inch plywood with a saw.
Brush wood glue onto one plywood surface and place the other piece onto it, creating a tabletop that is 2 inches thick. Clamp the pieces together and allow the glue to dry for the time recommended on the bottle.
Cut five 2-foot pieces of 2-by-4 boards.
Stand the board pieces on their narrow edges across the 2-foot length of the tabletop, dividing it into four equal portions. Flip the entire assembly upside-down so the plywood rests on the board pieces.
Drill four 1/16-inch pilot holes through the plywood and into each board piece. There will be 20 pilot holes in total.
Screw the boards to the plywood with 4-inch wood screws inserted into the pilot holes.
Turn the table right side-up.
Cut 10 12-inch pieces of 2-by-2 boards.
Stand a piece of 2-by-2 board next to each cut end of the 2-by-4 boards. These will form a cage that prevents the logs from rolling off of the table.
Drill two pilot holes through each 2-by-2 board and into the corresponding 2-by-4 board.
Secure the boards together with 3-inch wood screws.
Place the table onto two sawhorses to raise it to working height.