Question

fill in the blanks so that the resulting statement is true. using interval notation, the domain of f(x) = \log_{b}x is \square and the range is \square.

Explanation:

Step1: Recall Domain of Logarithmic Function

The logarithmic function \( f(x) = \log_b x \) is defined only when the argument \( x \) is positive. So, \( x > 0 \). In interval notation, this is \( (0, \infty) \).

Step2: Recall Range of Logarithmic Function

For any base \( b > 0, b
eq 1 \), the logarithmic function \( \log_b x \) can take on any real number value. So, the range is all real numbers, which in interval notation is \( (-\infty, \infty) \).

Answer:

The domain is \((0, \infty)\) and the range is \((-\infty, \infty)\).