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The domain of the parent logarithmic function is all positive real numbers, and the range is all real numbers.

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The parent logarithmic function is typically represented as f(x) = \log_b(x) , where b is the base of the logarithm and x is the argument of the logarithm.1. Domain: The domain of a function is the set of all possible input values (arguments of the function) for which the function is defined. For the parent logarithmic function, the logarithm is only defined for positive real numbers. This is because the logarithm of a negative number or zero is undefined in the real number system. Therefore, the domain of the parent logarithmic function is all positive real numbers, which can be expressed as (0, \infty) in interval notation.2. Range: The range of a function is the set of all possible output values (values of the function). For the parent logarithmic function, as x takes on any positive real number, the output of the logarithm can take on any real number. This means that the range of the parent logarithmic function is all real numbers, which can be expressed as (-\infty, \infty) in interval notation.In summary, the domain of the parent logarithmic function is all positive real numbers, and the range is all real numbers.

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