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

Explaining the answer: The logarithmic function in question, with a base of 7, is defined by the set of all possible x values for which y is defined. This function is valid for log x > 0, which means x must be greater than 0. Therefore, the domain is x ∈ (0,∞). The range is defined by the values of y corresponding to the defined x, resulting in a range of y ∈ (0,∞). The inverse function can be derived by swapping x and y in the original equation, yielding: Thus, the inverse also confirms that both x and y are greater than 0.

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