The Windows Update Client maintains its own log of installed updates. Rather than querying the generic system event log, or actively searching for updates which can take some time, here is example code to query and read the installation history from your Windows Update Client:
$Session = New-Object -ComObject Microsoft.Update.Session
$Searcher = $Session.CreateUpdateSearcher()
$HistoryCount = $Searcher.GetTotalHistoryCount()
Select-Object Date, Title, Description, SupportUrl
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These little pieces of code sometimes are pure GOLD.