Why do you have to turn on the hair dryer to use your microwave?

Answer for USA, Canada and countries running a 60 Hertz supply service.It sounds like the hair dryer wiring is in series with the microwave circuit. This can be very serious in some situations as the current for one device will be flowing through the second device. This could be caused by an open neutral on a three wire circuit. The hair dryer is on one side of the circuit to neutral and the microwave is on the other side of the circuit. With no return to the neutral bar the one device has to depend on the second device to close the circuit to operate. Check for an open neutral in the first junction box that is fed from the distribution panel. The open neutral could also be in the distribution panel. Check the breakers that feed the plugs that the devices are plugged into. It should be a three wire red, black and white cable set. See if the white is connected to the neutral bar. An electrician should be able to correct this condition on a service call.

Before you do any work yourself,

on electrical circuits, equipment or appliances,

always use a test meter to ensure the circuit is, in fact, de-energized

IF YOU ARE NOT REALLY SURE YOU CAN DO THIS JOB

SAFELY AND COMPETENTLY

REFER THIS WORK TO QUALIFIED PROFESSIONALS.