What are the domain and range of the logarithmic function f(x) = log7x? Use the inverse function to justify your answers.

Answer:

The logarithmic function f(x) = log7(x) has a domain of x > 0 and a range of all real numbers. This can be justified by its inverse function, g(x) = 7^x. The domain of an exponential function like 7^x is all real numbers, and its range is y > 0. Since the domain of a function is the range of its inverse and the range of a function is the domain of its inverse, the domain of f(x) is x > 0 and the range of f(x) is all real numbers.