How can a drug have a longer duration than half-life?

I noticed that many drugs have a longer duration than half-life? How is it possible for the drug to be still working when it was long gone excreted from the body?
Half life is the time it takes the body to excrete half of the drug out of the body. The remaining half of the dose still has an effect (although diminished) until all of the drug is finally excreted.

Just because half the drug has been excreted/inactivated it doesn't mean that the remaining half doesn't still have an effect. I believe almost if not all half lives are logarithm so there is a prolonged decay after the half life.

ok that clears it up thank you