Proof of Binary Search runtime

How do we prove the respective runtime for this?

Induction (mentioned in discrete math)
1. Start with an informed guess. $T_{ss} (n) = C_{rs} l o g_{2} (n) + C_{ss}$
2. Basis $C_{rs} l o g_{2} (1) + C_{ss} = C_{ss}$ 0 + $C_{ss} = C_{ss}$
3. Induction (n > 1): Assume the statement is true for $n^{'} < n$ (Inductive Hypothesis)
$T_{ss} (n) = C_{rs} + T_{ss} (\frac{n}{2})$ $=$ $C_{rs} + C_{rs} l o g_{2} (\frac{n}{2}) + C_{ss}$ $= C_{rs} + C_{rs} (l o g_{2} (n) - l o g_{2} (2)) + C_{ss}$ $= C_{rs} l o g_{2} (n) + C_{ss}$

(¬_¬")