Find if column exist in certain tables
This will give you the Schema and Table names along with YES or NO and Creation date:

SELECT s.name As [Schema]
    , t.name as [Table]
    , CASE WHEN c.name IS NULL THEN 'NO' ELSE 'YES' END as 'Exists'
    , t.create_date
FROM sys.tables t
INNER JOIN sys.schemas s ON t.schema_id = s.schema_id
LEFT JOIN sys.columns c ON c.object_id = t.object_id AND c.name = 'test' 


How the master table works is unclear but it seems that adding such a WHERE clause should work:

WHERE t.name IN (
    SELECT tn.name + CAST(mn.id as varchar(10)) as name
    FROM (values('Logs'), ('Details'), ('Data')) as tn(name)
    CROSS JOIN [master] mn
)


This will mix the list of name with the list of ids from master. Names can be added to the list or it could be replaced by a Names table.

By the way, master is not a proper name for a table since it is also a system database name.

This query adds productname from sample @master table for id &lt; 5:

declare @master table (id int, productname varchar(10))
insert into @master(id, productname) values(1, 'xxx'), (2, 'yyy'), (6, 'yyy')

SELECT s.name As [Schema]
    , t.name as [Table]
    , CASE WHEN c.name IS NULL THEN 'NO' ELSE 'YES' END as 'Exists'
    , t.create_date
    , m.productname
FROM sys.tables t
INNER JOIN sys.schemas s ON t.schema_id = s.schema_id
INNER JOIN (
    SELECT name = tn.name + CAST(mn.id as varchar(10)) 
        , mn.productname
    FROM (values('Logs'), ('Details'), ('Data')) as tn(name)
    CROSS JOIN @master mn
    WHERE mn.id &lt; 5
) m ON m.name = t.name
LEFT JOIN sys.columns c ON c.object_id = t.object_id AND c.name = 'test'