find the domain of the function y=2+log(x-1)

i need help finding the domain of a function
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The domain relates to the range of permissible values for x. Since we cannot evaluate logs of negative numbers, x-1>0 so x>1. When 1<x<2, the log < 0 so y<2 including negative values, for this range of x. When x>2, y>2.

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