The number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree.
Let assume number of nodes in right subtree is r and for left subtree number of nodes are l.
then for left subtree number of nodes ranges from ..
$r/2\leqslant l\leq 2r$
and root contains 1 node.
root node+ left subtree nodes+ right subtree nodes= n
So, 1+r/2+r = n
3r/2 = n-1
Now, why we use r/2 because we want our tree to be maximum possible height that can only possible when we take minimum number of nodes.
LST = $(n-1)/3$
RST = $2(n-1)/3$
Now we can see that RST is multiplied by 2 means this part of the tree will cause the max height of the tree. which is log3/2(n).
Hence, answer is (D).