How to judge the relationship between the launch of new applications and user activity？

At present, I assume that they will be related, and I will collect the following data: For old users: 1. How many old users have logged into the system since the application went online? 2. What is the relationship between the login frequency and time of old users after the application is launched? If the login frequency of old users increases over time, it proves that the application improves user activity. Same for new users. Is there any other data to prove it? Welcome to supplement.