Output Log file using Paramiko in a Linux server

Question

I am writing a script that will get execute a few commands on the terminal using

stdin, stdout, stderr = ssh_client.exec_command('date')

I know that script screen.log will create a log file and on executing exit The output is logged. It works when I type it manually on the terminal but does not work when run using paramiko stdin, stdout, stderr = ssh_client.exec_command('script screen.log')

Attaching the complete code that I use.

import paramiko
import os.path
import sys
import requests
import subprocess
import logging

def passing(ans):

ssh_client=paramiko.SSHClient()

ssh_client.set_missing_host_key_policy(paramiko.AutoAddPolicy())

ssh_client.connect(hostname='devserver.com',username='username',password='password')




stdin, stdout, stderr = ssh_client.exec_command("script screen.log")

for x in range(len(ans)): 
    stdin, stdout, stderr = ssh_client.exec_command(ans[x])

stdin, stdout, stderr = ssh_client.exec_command("netstat")
stdin, stdout, stderr = ssh_client.exec_command("exit")

#stdin, stdout, stderr = ssh_client.exec_command("netstat")
logging.basicConfig()
logging.getLogger("paramiko").setLevel(logging.WARNING)
paramiko.util.log_to_file("screen.log")
cmd_output=stdout.read()
print(cmd_output)

passing(['script screen.log','netstat','ls','date','exit'])

This creates screen.log but does not write the output to screen.log.

It would be really appreciated if you could help me write the output to screen.log.