How can I use PowerShell to enable NTFS compression, in place, on log files older than x days?

The easiest solution, as PowerShell support for file operations is still rather lacking, is to create a PowerShell script to call the compact.exe utility and set it up as a scheduled task. Because of the space in the path name, you want to call compact.exe directly, instead of using Invoke-WMIMethod and the CIM_DataFile class (which will cause a lot of extra effort to deal with the space in the path).

Assuming an age of 3 days for X, your PowerShell script would look something like:

$logfolder="[location of the first logging subfolder]"
$age=(get-date).AddDays(-3)

Get-ChildItem $logfolder | where-object {$_.LastWriteTime -le $age -AND $_.Attributes -notlike "*Compressed*"} | 
ForEach-Object {
compact /C $_.FullName
}

$logfolder="[location of the next logging subfolder]"

Get-ChildItem $logfolder | where-object {$_.LastWriteTime -le $age -AND $_.Attributes -notlike "*Compressed*"} | 
ForEach-Object {
compact /C $_.FullName
}

...

The second condition there is to speed up the script execution by skipping over already compressed files (which would be present after the first time this script was run). If you wanted to, or had a lot of different logging subfolders, it would probably make sense to make a function out of that repeated PowerShell code, which would be a fairly trivial exercise.

The repeated code can be avoided by using an array and a foreach loop:

$logfolders=("D:\Folder\One","D:\Folder\Two")
$age=(get-date).AddDays(-3)

foreach ($logfolder in $logfolders) {
    Get-ChildItem $logfolder | where-object {$_.LastWriteTime -le $age -AND $_.Attributes -notlike "*Compressed*"} | 
    ForEach-Object {
    compact /C $_.FullName
    }
}

.....

Invoke-WmiMethod -Path "Win32_Directory.Name='C:\FolderToCompress'" -Name compress

It is possible to do this without needing to rely on compact.exe, a "pure powershell" method by calling the NTFS compression directly. This handles spaces in file names and unicode filenames from Japan as well, the latter are difficult to supply to a compact.exe command line. See https://docs.microsoft.com/en-us/windows/win32/api/winioctl/ni-winioctl-fsctl_set_compression as well.

$MethodDefinition= @'
public static class FileTools
{
  private const int FSCTL_SET_COMPRESSION = 0x9C040;
  private const short COMPRESSION_FORMAT_DEFAULT = 1;
  private const short COMPRESSION_FORMAT_DISABLE = 0;

  [DllImport("kernel32.dll", SetLastError = true, CharSet = CharSet.Unicode)]
  private static extern int DeviceIoControl(
      IntPtr hDevice,
      int dwIoControlCode,
      ref short lpInBuffer,
      int nInBufferSize,
      IntPtr lpOutBuffer,
      int nOutBufferSize,
      ref int lpBytesReturned,
      IntPtr lpOverlapped);

  public static bool Compact(IntPtr handle)
  {
    int lpBytesReturned = 0;
    short lpInBuffer = COMPRESSION_FORMAT_DEFAULT;

    return DeviceIoControl(handle, FSCTL_SET_COMPRESSION,
        ref lpInBuffer, sizeof(short), IntPtr.Zero, 0,
        ref lpBytesReturned, IntPtr.Zero) != 0;
  }
  public static bool Uncompact(IntPtr handle)
  {
    int lpBytesReturned = 0;
    short lpInBuffer = COMPRESSION_FORMAT_DISABLE;

    return DeviceIoControl(handle, FSCTL_SET_COMPRESSION,
        ref lpInBuffer, sizeof(short), IntPtr.Zero, 0,
        ref lpBytesReturned, IntPtr.Zero) != 0;
  }
}
'@

$Kernel32 = Add-Type -MemberDefinition $MethodDefinition -Name ‘Kernel32’ -Namespace ‘Win32’ -PassThru

$logfilespec = "c:\Logfolder\*.log"

# compact anything older than three days
foreach ($File in (Get-ChildItem -Path $logfilespec -Recurse -File).Where({$_.LastWriteTime -lt (Get-Date).AddDays(-3) -and $_.Attributes  -notmatch [System.IO.FileAttributes]::Compressed})) {
    $FileObject = [System.IO.File]::Open($File.FullName,'Open','ReadWrite','None')
    $Method = [Win32.Kernel32+FileTools]::Compact($FileObject.Handle)
    $FileObject.Close()
}

# decompact
foreach ($File in (Get-ChildItem -Path $logfilespec -Recurse -File).Where({$_.Attributes  -match [System.IO.FileAttributes]::Compressed})) {
    $FileObject = [System.IO.File]::Open($File.FullName,'Open','ReadWrite','None')
    $Method = [Win32.Kernel32+FileTools]::Uncompact($FileObject.Handle)
    $FileObject.Close()
}

If those log files are not on C: use the Server 2012 R2 deduplication feature. You can then configure it to only dedup .log files which are three days old (the default). The second method to get this under control, or when it is on C: Move the log directory to a different drive and use a JUNCTION to point to the new place, easiest to create with Hardlink-Shell-Extension from https://schinagl.priv.at/nt/hardlinkshellext/linkshellextension.html - and then use 2012 R2 deduplication on top. I've see deduplication rates way above 90% on log files and the SQl-dump-for-backup drives.