Robopurging expired files
To reduce the amount of log files I would keep things in memory:

$Log = "C:\scripts\list.txt"
$purged = "C:\scripts\purged.txt"
$now = Get-Date
$days = "7"
$Lastwrite = $now.AddDays(-$days)
$datetime = get-date -f MM-dd-yy-hhmmtt

#Robocopy will automatically overwrite the log file unless you specifiy /log+:
robocopy "c:\downloads" "c:\downloads1" /e /Purge /R:1 /W:1 /l /TEE /FP /LOG:"$log" /MT:16 

#Save purged log
rename-item $purged ($purged -replace('.txt', "_$datetime.txt"))

Get-Content $Log | foreach {

    #Split columns by tab
    $fileType =  ( $_ -split("`t") )[1]
    $filePath =  ( $_ -split("`t") )[2]


    if ( ($fileType -like "*Extra File*") -or ($fileType -like "*Extra Dir*") ){
        if ( (Get-Item $filePath).LastWriteTime -le $Lastwrite){
            "Deleting File: $filePath" | Out-File $purged -Append
            remove-item $filePath -WhatIf -Recurse
        }
    }

}