  Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality
(RLBM).
  Secondly, we show that the (RLBM) conjecture is equivalent to the
log-Brunn-Minkowski (LBM) conjecture proposed by
B\"or\"oczky-Lutwak-Yang-Zhang. We name this as ``reverse-to-forward
principle". Using this principle, we give a very simple new proof of the
log-Brunn-Minkowski inequality in dimension two.
  Finally, we establish the ``reverse-to-forward principle" for the
log-Minkowski inequality (LM).Using this principle, we prove the log-Minkowski
inequality in the case that one convex body is a zonoid (the inequality part
was first proved by van Handle). Via a study of the lemma of relations, the
full equality conditions (``dilated direct summands") are also characterized,
which turns to be new.
