Viewing the SQL server log file

What is the purpose of view the transaction log file for a database?

You can take help of undocumented statement such as: DBCC LOG(<databasename >, <type of output>)

<type of output>
0: Return only the minimum of information for each operation -- the operation, its context and the transaction ID. (Default)
1: As 0, but also retrieve any flags and the log record length.
2: As 1, but also retrieve the object name, index name, page ID and slot ID.
3: Full informational dump of each operation.
4: As 3 but includes a hex dump of the current transaction log row.

Have a look at fn_dblog and in order to get full information you must depend on third party toll such as Log Explorer or Quest log reader or look at ApexSQL tool from http://www.apexsql.com/sql_tools_log.asp.

I don't think a log viewer is the right choice for such a scenario. What about Change Data Capture?

True, as suggested by Frank you must deploy the programming methods using TSQL to obtain such information, it will rather allow you to alert if there si a certain issue with the desiered tables. Lets say if you have used third party tools then you should continue this doing all the times.
have a look at SQL Server books online for CDC concept.

Yes it will log the transactions and as per BOL (see Frank's link) too:
Both the capture and cleanup jobs are created by using default parameters. The capture job is started immediately. It runs continuously, processing a maximum of 1000 transactions per scan cycle with a wait of 5 seconds between cycles. The cleanup job runs daily at 2 A.M. It retains change table entries for 4320 minutes or 3 days, removing a maximum of 5000 entries with a single delete statement.

I believe you need to take your time to study and know about CDC to fulfil the requirement, have a look at SQL Server Books online for more information.