The logarithmic Chow (semi)stability is defined for the pair consists of polarized complex manifolds and its divisors. In this talk, I will introduce a obstruction of semistability of polarized toric manifolds and its toric divisors. As its application, I will also introduce the followings.

   (1) A relation between the log Chow semistability and the log K-semistability which is expected to be equivalent to the existence of canonical Kahler metrics on polarized complex manifolds. 

   (2) Calculation of this obstruction for a few example and relation to the existence of conical Kahler Einstein metrics.

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