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Domain of a log graph

The function g has rule g(x) = loge|x- b|, where b is a real constant.
The maximal domain of g is

I got (b,infinity) but the answer was R{b}. Could anyone explain what the | | actually does to the equation? Thanks

|...| is a modulus operation. Basically: the modulus will take any negative number, and make it into a positive number of the same magnitude.
Assuming the following equation x = |-2|, we could simplify x to x = 2. A graph of y = |x| is a modulus function and doesn't look like a normal y = x function. Instead, it will look like the following: