How can I find out when an app was downloaded?

Hi.

Is there any way of telling when an app was downloaded even after it has been deleted? Better yet, is there any way of getting a log of activity from the app store to see download history with dates?

I know I can go into 'purchase history' > 'not on this phone' to see when updates were released for previously deleted apps, but it doesn't tell me when the apps were downloaded or deleted.

Thanks