C 分析:根據(jù)函數(shù)y=loga x (a>1)的圖象必過定點(0,1),由此可得函數(shù)y=loga(x-1)+1(a>1)的圖象必過的定點. 解答:由于函數(shù)y=loga x (a>1)的圖象必過定點(0,1), 故函數(shù)y=loga(x-1)+1(a>1)的圖象必過定點(2,1), 故選C. 點評:本題主要考查對數(shù)函數(shù)的單調(diào)性和特殊點,利用了函數(shù)y=loga x (a>1)的圖象必過定點(0,1),屬于中檔題.