I can't tell you from Ahri's perspective, but I can tell you from a tank's perspective.
First of all (even though a lot of people already pointed this out) mages aren't supposed to take on tanks. In fact, anyone with burst is supposed to avoid wasting their combos in tanks since they'll be left with cooldowns. In teamfights, it's the ADCs job to kill the tank since auto-attacks are unlimited and AD assassins can't often go toe-to-toe with a tank. As a mage, your job is to deal AOE damage to the entire enemy team.
Now, if you're laning against one, your best bet is to outpoke them but make sure your mana remains at a good amount. Just remember that your jungler is your best friend. Try and get an early gank to kill them before they start building hp and resistances or you won't be able to later. If you successfully keep them from farming, they should be left without enough hp and resistances. Just remember to never all-in them unless you're absolutely positive you can finish them off because they can take a lot more hits than Zed.