The exchange logs can to take up a fair amount of space.
In order to minimise the log sizes you can enable circular logging. there are warnings here about why you shouldn’t related to incremental backups not working etc.
If you want to enable circular logging any way
Open exchange management console
Right click and select properties on the mailbox store you want to enable circular looking for
Go to the maintenance tab
Check on enable circular logging
Dismount and remount the –