.Demailly, Ein and Lazarsfeld [3] formulated a subadditivity property of multiplierideals on nonsingular varieties, which states that the multiplier ideal of the prod-uct of two ideal sheaves is contained in the product of their individual multiplierideals. Their formula has many interesting applications in algebraic geometry andcommutative algebra, such as Fujita’s approximation theorem (see [7] and [11, The-orem 10.3.5]) and its local analogue (see [5]), a problem on the growth of symbolicpowers of ideals in regular rings (see [4]), and etc. Later, Takagi [16] and Eisenstein[6] generalized their formula to the case of Q-Gorenstein varieties, that is, the casewhen ∆ = 0 in the above definition of multiplier ideals. In this article, we studya further generalization to the case of log pairs, when the importance of multiplierideals is particularly highlighted. The following is our main result.Theorem (Theorems 2.3 and 3.5). Let Xbe a normal variety over an algebraicallyclosed field of characteristic zero and ∆ be an effective Q-divisor on X such thatr(K