Hallux is right, some launchers let you create a widget to access the notification log. Just in case, long press an empty spot on your home screen - tap 'widgets' - scroll down until you find 'settings 1x1' - press & hold and drag it to the screen - select 'notification log' from that list.
If this option is not available in your phone you can use a custom launcher like Nova or a widget creator app like More Shortcuts.