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

Answer:

The inverse of the logarithmic function f(x) = log7(x) is the exponential function g(x) = 7^x. For the exponential function g(x) = 7^x, the domain is all real numbers (-∞, ∞) and the range is all positive real numbers (0, ∞). Because 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) = log7(x) is all positive real numbers (x > 0) and the range is all real numbers (-∞, ∞).