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In order to investigate the boundedness or compactness of composition operator from the logarithmic Bloch-type space to the Bergman space on the unit polydisc,the classic Bergman norm is firstly changed into another equivalent norm.Then according to some common inequalities,the properties of logarithmic Bloch-type space and the absolute continuity of the general integral,the conditions which the symbol map must meet when the composition operator is bounded or compact are obtained after a series of calculations,and the boundedness and compactness are proved to be equivalent.