There are many myths and false lore surrounding mountain biking. One common misconception is that the best way to make any tight turn is to lock up the rear wheel and skid it around. Stay back as needed with the heaviest braking before the apex. Trials riders might have their hips above the bars in one moment and their sternum over the seat in the next. Just like in skiing, your feet are the final connection between body and bike and any jumping or pressure control begins there.
Larger objects require precision timing and advanced momentum and weight management skills.
Jumping the object is often the best bet, but does require advanced bunny hop skills and enough momentum, something that is not always possible on a winding singletrack . There are two other alternatives short of riding around or carrying over. If you miss the retraction part, or on the larger logs, you will feel the chainring contact. It's also very important to have your momentum traveling straight ahead, and don't fall to the side, as this will result in a bent chainring. As your chain ring leaves the log, make sure the front wheel moves forward by thrusting your arms forward and staying light on your hands to avoid the back side endo.