Height of epsilon-balanced binary search tree

Question

In Balanced Binary Search Trees on the basis of size of left and right child subtrees, Hannes says:

For example, one can say, a BST is balanced, if each subtree has at most epsilon * n nodes, where epsilon < 1 (for example epsilon = 3/4 or even epsilon = 0.999 -- which are practically not balanced at all). The reason for that is that the height of such a BST is roughly log_{1/epsilon}

I am a bit puzzled on the last statement -- how do we know that the height is roughly 1/epsilon?