Copy the following script to Powershell file on a mailbox server in your environment and then execute it as needed from the Exchange Management shell.
$MDBs = Get-MailboxDatabase -Status | Select Name,Server,Mounted
Foreach($MBX in $MDBs){
If($MBX.Mounted -eq $false){
Write-Host $MBX.Name " " $MBX.Server " " $MBX.Mounted -BackgroundColor Red
}else{
Write-Host $MBX.Name " " $MBX.Server " " $MBX.Mounted
}
}