app1logfolder
|-app1_20130507.log
|-app1_20130508.log
|-app1_20130509.log

app2logfolder
|-app2_20130507.log
|-app2_20130508.log
|-app2_20130509.log

logs_20130507.zip
|-app1_20130507.log
|-app2_20130507.log

logs_20130508.zip
|-app1_20130508.log
|-app2_20130508.log

logs_20130509.zip
|-app1_20130509.log
|-app2_20130509.log

# load the assembly required
[Reflection.Assembly]::LoadWithPartialName("System.IO.Compression.FileSystem")
$sourceFolder = "C:PathToYourLogs"
$destinationFile = "C:PathToYourDestination.zip"
# desired compression level (Optimal, Fastest or NoCompression)
$compressionLevel = [System.IO.Compression.CompressionLevel]::Optimal
# include the directory $sourceFolder or just it's contents
$includeBaseDirectory = $false

[System.IO.Compression.ZipFile]::CreateFromDirectory($sourceFolder, $destinationFile, $compressionLevel , $includeBaseDirectory)

$date_string = Get-Date -Format 'yyyyMMdd'

$zip_filename = "logs_$date_string.zip"

# Create the empty zip file
Set-Content $zip_filename ( [byte[]] @( 80, 75, 5, 6 + (, 0 * 18 ) ) ) -Encoding Byte

$zip_file = Get-Item -Path $zip_filename | ForEach-Object {

    (New-Object -ComObject Shell.Application).NameSpace($_.FullName)
}

[array]$log_files = Get-ChildItem -Recurse -Filter "*_$date_string.log"

for ($i=1; $i -le $log_files.Count; $i++) {

    $zip_file.CopyHere($log_files[$i-1].FullName)

    # Copying is async so we need to check if it is done before continuing.
    while ($zip_file.Items().Count -ne $i) { sleep 0.1 }

}