  In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of
the first kind and recall multi-Bernoulli numbers, all of whose generating
functions are given with the help of multiple logarithm. The aim of this paper
is to study several relations among those three numbers. In more detail, we
represent the multi-Bernoulli numbers in terms of the multi-Stirling numbers of
the first kind and vice versa, and the multi-Lah numbers in terms of
multi-Stirling numbers. In addition, we deduce a recurrence relation for
multi-Lah numbers
