who said we always deal with log base 2 only in computer science!! most of the topic in gate syllabus are concerned about binary trees so we say that we always use log base 2.have you thought about b-trees and b+ trees there we have the base m concept where m is the order of tree .incase of binary tree m is always 2 so we use base 2 try to evaluate the height of a binary tree when number of nodes are given and the height of a m-ary tree when number of nodes are given you have to use log base 2 and log base m respectively