Do you want only the last log?
What if you prepare a file for overwriting separately from the log file output (append)?
The file is always overwritten at the timing of log output.

I am sorry if the intention is different.

What about thetailcommand?

I don't really answer questions that don't have a code at all ...
python doesn't work unless the indentation is correct

tail-like implementation (3 lines)

import sys
import collections
deque = collections.deque (maxlen = 3)
for line in sys.stdin.readlines ():
    deque.append (line)
for line in deque:
    print (line, end = "")