List installed applications on remote servers - powershell

Question

I have pieced together the following script which lists all installed applications on a local system and writes it into a logfile, but I am unaware how to get this same output when using PSRemoteRegistry, the actual input list I need this against will be all remote targets.
Does anyone have experience with fitting this same code into the cmdlets available through PSRemoteRegistry? Specifically I need it to enumerate the displayname of every installed app found in the key HKLM:\Software\Microsoft\CurrentVersion\Uninstall
The piece I am needing help with getting into the PSRemoteRegistry cmdlets is:
Get-ChildItem 'HKLM:\Software\Microsoft\Windows\CurrentVersion\Uninstall' | ForEach-Object {Log (Get-ItemProperty $_.pspath).DisplayName}
and this is the entire script:
clear
#$ErrorActionPreference = "silentlycontinue"
$Logfile = "C:\temp\installed_apps.log"
Function Log
{
param([string]$logstring)
Add-Content $Logfile -Value $logstring
}
$target_list = Get-Content -Path c:\temp\installed_apps_targets.txt
foreach ($system in $target_list){
if (test-connection $system -quiet)
{
Log "---------------Begin $system---------------"
Get-ChildItem 'HKLM:\Software\Microsoft\Windows\CurrentVersion\Uninstall' | ForEach-Object {Log (Get-ItemProperty $_.pspath).DisplayName}
Log "---------------End $system---------------"
}
else
{
Log "**************$system was unreachable**************"
}
}

Answer 1

You can adapt something like this:
$Computer = "ComputerName"
$Reg = [Microsoft.Win32.RegistryKey]::OpenRemoteBaseKey('LocalMachine', $Computer)
$RegKey= $Reg.OpenSubKey('Software\Microsoft\Windows\CurrentVersion\Uninstall')
$Keys = $RegKey.GetSubKeyNames()
$Keys | ForEach-Object {
$Subkey = $RegKey.OpenSubKey("$_")
Write-Host $Subkey.GetValue('DisplayName')
}

Answer 2

Have you met Invoke-Command?
$Logfile = "C:\temp\installed_apps.log"
Function Log() {
param([string]$logstring)
Add-Content $Logfile -Value $logstring
}
$scriptbock = {Get-ChildItem 'HKLM:\Software\Microsoft\Windows\CurrentVersion\Uninstall' | ForEach-Object {Log (Get-ItemProperty $_.pspath).DisplayName}}
Get-Content -Path c:\temp\installed_apps_targets.txt | % {
if (test-connection $_ -quiet) {
Log "---------------Begin $system---------------"
Log $(Invoke-Command -ComputerName $_ -ScriptBlock $scriptblock)
Log "---------------End $system---------------"
}
else
{
Log "**************$system was unreachable**************"
}
}