Multiple python processes logging to same file

multi_process_log_test.py

from multiprocessing import Process, Manager
import time 

number_of_processes = 1000

# Current time in milliseconds since epoch
def getCurrentTimeInMilliSeconds():
    return int(time.time() * 1000)

def produce(i):
	print(f"Started producer number {i}")
	while True:
		time.sleep(0.1)
		with open("test_multi.log", "a") as f:
			f.write(f"{getCurrentTimeInMilliSeconds()}: Produced by {i}\n")
	pass

if __name__ == '__main__':
	print("MultiProducer log to same file")

	process_manager = Manager()
	
	producer_processes = []
	for i in range (1, number_of_processes):
		producer_process = Process(target=produce, args=([i]))
		producer_processes.append(producer_process)
		producer_process.start()

	for process in producer_processes:
		process.join()