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 $\square$.
Answer
Final Answer: The domain of \(f(x)=\log _{b} x\) is \(\boxed{(0, \infty)}\) and the range is \(\boxed{(-\infty, \infty)}\).
Step 1 ：The domain of a logarithmic function is the set of all positive real numbers. This is because you can only take the logarithm of a positive number. In interval notation, this is represented as (0, ∞).
Step 2 ：The range of a logarithmic function is the set of all real numbers. This is because the logarithm of a number can be any real number. In interval notation, this is represented as (-∞, ∞).
Step 3 ：Final Answer: The domain of \(f(x)=\log _{b} x\) is \(\boxed{(0, \infty)}\) and the range is \(\boxed{(-\infty, \infty)}\).
