Answer with explanation:
The given logarithmic function whose base is, 7 is
[tex]y=f(x)=\log_{7}x[/tex]
Domain of a function is defined as, set of all possible values of , x , for which ,y is defined.
[tex]\log_{7}x=\frac{\log x}{\log 7}[/tex]
is defined for,
→ log x > 0.
⇒ x ∈ (0,∞)
And range of a function is defined as those values of y, for which x, is defined.
[tex]y=\log_{7}x\\\\y=\frac{\log x}{\log 7}\\\\ \log x =y \log 7\\\\x=7^y[/tex]
So, Range = y∈ (0,∞).
The inverse of the above function can be obtained by, replacing, x by y, and y by x , in the above equation:
So, the inverse of the above function is :
[tex]y=7^x[/tex]
Here, x ∈ (0,∞) and, y ∈ (0,∞).
