It is there in the app, but you are using the browser.
In the browser on my iPhone (don't have my old iPad with me at the moment) there is an Activity Log button (gray circle with 3 dot/lines in it) under my name. I also don't have the Edit Profile button that you have.
You should also be able to find it by tapping the three bars on the top right of the main Facebook page, scroll down to Settings, scroll down to the Your Facebook Information section and tap on Activity Log.
Tapping the same button again isn't really following instructions given.
Here they are again broken down even more:
Try going to your Facebook feed
Tap the 3 bars (3 lines) in the top right side
Scroll down and tap on Settings
Scroll down to the Your Facebook Information section and tap on Activity Log