Pandas index match without merge

Question

So I have two dataframes. activity_log records when a client logs in based on their client_id. A client_id can appear multiple times given the client logs in multiple times over a period.

I need to create a third column in this activity_log looks up the date that the client was created. This created_date is calculated by looking at the earliest user_created date in the user_table.

activity_log

client_id	activity_date	created_date
1	12/12/2022
1	11/12/2022
1	9/12/2022
1	8/12/2022
2	12/12/2022
2	11/12/2022
3	10/12/2022
3	9/12/2022

user_table

client_id	user_id	user_created
1	12asdasd3	12/12/2021
1	1sads23	11/12/2021
1	asasdsa2	10/12/2021
2	32asdasd1	12/12/2021
2	3asdasd21	11/12/2021
3	1asdsaa22	2/12/2021

I have tried using pandas merge

activity_log.merge(client_table[['client_id','user_created']], how='inner', on='client_id')

The problem with this is that I end up with a table that is grater in size than the original activity_log because the client_id appears multiple times in the activity_log and multiple times in the user_table.

I want to look up the client_id in the user_table, get the earliest user_created value and put that into the created_date column in the activity_log.

Any ideas on what else I need to do to achieve this?