That is a Strictly Increasing Function and a special case of Jensen's inequality for convex functions. The logarithm function is concave, and Jensen's inequality tells us that for a concave function, the function's value at the average point is greater than or equal to the average of the function's values.

On the contrary, if we consider the situation with a convex function, the value of the function at the average point will be less than or equal to the average of the function’s values.