To see the download history (I believe this should be any version of iOS):
First, open your app store and tap on your profile in the top right.
After that, go to Purchase History (I know, you might say “I want to see my download history, not this.” Don’t worry, it’s coming; they’re classified as free purchases.)

If you’re like me and don’t spend money on apps (or at least not recently), it will be blank. The filter is defaulted to last 90 days, paid. Click that blue text, or “Change Filters.”

Depending on what you want to filter to, from the drop downs, you can set filters or just check everything, then press the check mark. A list will appear and you can see the app or purchase, the date, and the price.