Welcome to the Forum @Ashraf_El_Jurdi and thank you for reaching out!
As it stands, there isn’t a built feature that records the project log. You could use the Advanced Search tool to create reports to track some of the activities within a project or you could use [Portfolio] feature (https://asana.com/guide/help/premium/portfolios) to track the progression of your project.
There are a few threads in the #productfeedback category regarding this topic. I would encourage you to cast your vote and comment on the ones you you would like to see implemented:
Please let me know if you have any follow-up question Ashraf! Have a nice day!