Question

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

Answer 1

Step-by-step explanation: The domain of a function is the set of all values for which the function is defined and the range is the set of all values
`y`, for which there exists some
`x` such that

`y=f(x)=\log7x\\\Rightarrow 7x=10^y\\\Rightarrow x=10^y/7`.

Since
`log x` is defined for all real values of
`x` greater than zero. So, the domain of the given function is

D=7x is a real number>0=x is a real number>0.

And range is given by

R=y=\log 7x=y is a real number.

Thus, the domain is the set of all positive real numbers and range is the set of all real numbers.

Answer 2

Explanation:

Since log is defined by all positive real numbers

therefore domain is all positive real number that is ( 0,∞)

Range is given by real numbers

inverse of the given function is (10^x)/7

Whose domain is all real numbers and range is all positive real number

And since we know that domain of function and range of its inverse

& range of a function and domain of its inverse is same

which we are getting in the problem

so answer is justified