Will write only output was instructed with >>.
If need to all out put use start-transcript and stop-transcript
set-location "C:\Temp"
$dateinfo = get-date -Format "MMddyyy_HHmmss"
$logfilename = "log" + $dateinfo + ".log"
get-date >> $logfilename
write-output "Script starting...." >> $logfilename
Get-Process | select -First 5 >> $logfilename
get-date >> $logfilename
Write-Output "Script end!" >> $logfilename
Output in .log file
Sunday, May 7, 2023 7:27:11 PM
Script starting....
Handles NPM(K) PM(K) WS(K) CPU(s) Id SI ProcessName
------- ------ ----- ----- ------ -- -- -----------
1585 44 58264 29464 132.52 9492 2 1Password
248 14 12824 8236 2.30 16148 2 1Password
945 28 96832 10952 12.23 28976 2 1Password
245 16 7208 6428 1.58 17304 2 1Password-BrowserSupport
1043 51 64340 29144 28080 0 Agent
Sunday, May 7, 2023 7:27:11 PM
Script end!