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The height of a binary tree is defined as the number of nodes in the longest path from root to the leaf node. Let X be the height of a complete binary tree with 256 nodes. Then the value of X will be

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https://www.geeksforgeeks.org/relationship-number-nodes-height-binary-tree/

If there are n nodes in a binary tree, the maximum height of the binary tree is n-1 and minimum height is $\left \lfloor log\ 2n \right \rfloor$ .

Read carefully what it is saying :- The height of a binary tree is defined as the number of nodes in the longest path from root to the leaf node. i.e. if node is 3 with (height 2) then height = 3 (a/c to question).

basically it is saying with node = 1 height = 1.

now, for complete binary tree h= ceil(log(n+1)-1) [with height starting from h=0 with node=1.]

ceil(log(256+1)-1=8

hence for this question 8+1= 9.

by

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@  I think you have wrongly taken the formula. In question its mentioned that complete tree with total  256 nodes. The height of complete binary tree is floor value (log n+1)  with base 2. Hence height should be 8

Please refer underlined part of the image

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