Efficient way to get last record from the database

I have a database with following table structure :

id | entry | log_type  | user_id | created_on   |
------------------------------------------------|
1  |a      | error     | 1       | 1433752884000|
2  |b      | warn      | 2       | 1433752884001|
3  |c      | error     | 2       | 1433752884002|
4  |d      | warn      | 4       | 1433752884003|

I want to obtain the last record from the table based on created_on field, currently i am using the following query to obtain the result list and obtain the last record on it using java:

select * from log_table l where l.user_id=2 and l.log_type = 'error' order by l.created_on desc;

I am using JPA and i execute the query using .getResultList() on the Query interface .Once i get the result list i do a get(0) to obtain the desired last record .

I have a large table with too much data , above query takes too long to execute and stalls the application. I cannot add additional index for now on existing data . Apart from adding the index on the data is there an alternate approach to avoid stalling of this query .

I was thinking of executing the following query,

select * from log_table l where l.user_id=2 and l.log_type = 'error' order by l.created_on desc limit 1;

Currently i cannot execute my second query on the database as it might cause my application to stall. Will execution of the second query be faster than the first query ?

I don't have a sufficiently large dataset available to reproduce the stalling problems on my local system and hence . I tried executing the queries on my local database and due to the lack of the available large dataset , unable to determine if the second query would be faster with the addition of "limit" on the returned query.

If the above second query isn't supposed to provide a better result , what would be the approach that i should to get an optimized query .

In case the second query should be good enough to avoid stalling , is it due to the reason that the DB fetches only one record instead instead of the entire set of records ? does the database handle looking/fetching for a single record differently as compared to looking/fetching too many records (as in first query) to improve query timings.