Final answer:
A private pilot can log the time as pilot-in-command when they are the sole manipulator of the controls of an airplane, regardless of being the actual aircraft commander.
Step-by-step explanation:
If you are a private pilot and the sole manipulator of the controls of an airplane, you can log the time as pilot-in-command (PIC) for the flight time during which you are the sole manipulator of the controls.
According to FAA regulations, a private pilot flying an aircraft for which the pilot is rated by the FAA, which in this case is an airplane, can log PIC time. Moreover, this time can be logged regardless of whether the pilot is the actual aircraft commander or not, as long as they are the person responsible for controlling the aircraft's flight in real time.