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In order to find the recurrence function of The Height in Heap, the following figure is drawn.

enter image description here

Question 1: How can we compute the height if Right subtree in form of Log in base 3, and why do we have the height of Left subtree as log in base 3/2?

Question 2: it is stated that:
“for a complete binary tree to have the maximum height the last level should be half full.”
i don’t grasp the logic behind this line.why?