Solution

n the case of a B-tree with a minimum number of keys, there is one key in the root, 2 nodes at depth 1 , 2tⁱ -1 nodes at depth i .   

Let h be the height of the tree and n be the number of nodes. Then

n>=1+(t-1) submission up h down i=1     2tⁱ-1

which works out to t^h<= (n+1) / 2. So we take the log_t of both sides.

 h <= log_t(n+1)/2 

Hence only h ≤ logt\(\rm\frac{n+1}{2}\) is correct.