Hover of the box with your name. Then it will show all the cards from you that are in special zones, including the Exile mat, where the log normally is. It also works for your opponent.
If there are so many cards in those zones that you can't see them all, you can click (or tap) on the box. That will make the display of those cards temporarily permanent, so you can move the mouse over and use the scroll bar.
If you are done looking at them, just click somewhere.