When a log has been floating for a long time it probably absorbs so much water that it begins to lose its ability to float.

When it reaches this point does it immediately sink to the bottom or does it slowly sink to the bottom.
My point is that I don't believe you could ever locate a log that was floating halfway between the surface and the bottom.

If I am right could you explain why?

Yes, logs do get "water logged" and sink lower into the water as they get heavier. It's not unusual for logs to be virtually entirely submerged, with just a little bit poking above the water - very dangerous for boaters and water skiers! If one end is heavier than the other for example, the log may end up being almost vertical in the water, or one end might be stuck in thd mud while the other is at the surface. But as for hovering under water, halfway between bottom and surface - no - this would require a perfect balance, which if it did occur would not last very long.