Because you will have enclosed the argument of the log function in parenthses, we assume you have ...
... f(x) = log₃(x -1) +3
The domain will be values of x that make the argument of the log function positive:
... x -1 > 0
... x > 1 . . . . . domain of f(x)
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The range is all real numbers, corresponding to the range of any log function.
