declare @dbName varchar(1024);
-- be sure to put your database name on the following line.
set @dbName = 'YourDatabaseName';

--declare @backup_set_id int;
declare @bfd datetime;
declare @fullbackup_file varchar(2048);

select top 1 
       @fullbackup_file = m.physical_device_name, 
       @bfd = b.backup_finish_date
 from msdb.dbo.backupset b
 JOIN msdb.dbo.backupmediafamily m 
   ON b.media_set_id = m.media_set_id
 where database_name = @dbName
   and type = 'D' -- type D = full database backup
 order by backup_set_id desc;
 

 select @fullbackup_file as backup_file_name, 
        @bfd as backup_finish_date
 union
 select m.physical_device_name as backup_file_name, 
        b.backup_finish_date
   from msdb.dbo.backupset b
   JOIN msdb.dbo.backupmediafamily m 
     ON b.media_set_id = m.media_set_id
  where database_name = @dbName
    and backup_finish_date > @bfd
    and type = 'L' -- type L = log backup
  order by backup_finish_date asc;