Zithromax has an elimination half-life of 68 hours.
The half life is used to estimate how long it takes for a drug to be eliminated from the body. Generally it takes 5.5 x half-life for a drug to be removed from the body, when it is deemed to no longer have an effect.
Therefore for Zithromax it would take about 374 hours (5.5 x 68 hours) which is 15.5 days to be removed from the body.

Elimination of a drug varies from person to person due to factors like age, weight, other medications taken, or other medical conditions present, also kidney function, liver function etc. Therefore half life is used as a guide or an estimate of how long it may take for the drug elimination.

For more information on Zithromax see:
https://www.drugs.com/pro/zithromax.html