Concatenating Variables within Powershell
You can use Join-Path and it will put in the directory slash for you.
$objWorkbook = $objExcel.Workbooks.Open (Join-Path $Log_path $Log_name)
It handles the logic if $Log_Path parent already has or doesn't have the slash.
>join-path c:\temp test.txt
c:\temp\test.txt
>join-path c:\temp\ text.txt
c:\temp\test.txt
$path = "C:\folder"
$name = "file.exe"
$fullname = $path + "\" + $name
$fullname
(or)
$fullname = "$path\$name"
but not
$fullname = '$path\$name'
Output
C:\folder\file.exe