Ternary Search Recurrence Relation
Hint: Recall what you are actually doing in ternary search - you basically partition the list into 2 parts, on of roughly $n/3$ elements, and the other of $2n/3$ elements. 

So, on a bad day (worst case) you do $2n/3$ recursive calls. 

Then the recurrence relation is $$T(n) = T(2n/3) + c $$

I'll cheat a bit here and use the master theorem to jump to the conclusion that $T(n) \in \Theta(log\ n)$