you may use simple query against msdb to get the information
select
database_name,
case type when 'L' then 'Log' else 'Data' end as Backuptype,
physical_device_name,
backup_start_date
from msdb.dbo.backupset a
join msdb..backupmediaset b on a.media_set_id = b.media_set_id
join msdb.dbo.backupmediafamily c on a.media_set_id = c.media_set_id
where type in ('L','D') -- L = Logbackup, D = Databackup
order by backup_start_date desc, database_name asc, Backuptype