The domain and range of the graph of a logarithmic function are;
The basic equation of a logarithmic function can be presented in the form;
[tex]y = log_{b}(x) [/tex]
Where;
b > 0, and b ≠ 1, given that we have;
[tex]y = log_{1}(x)[/tex]
[tex] {1}^{y} = 1[/tex]
The inverse of the logarithmic function is the exponential function presented as follows;
[tex]x = {b}^{y} [/tex]
Given that b > 0, we have;
[tex] {b}^{y} = x > 0[/tex]
Therefore, the graph of a logarithmic function has only positive x-values
The graph of a logarithmic function is one with a domain and range defined as follows;
Domain; 0 < x < +∞
Range; -∞ < y < +∞, which is the set of real numbers.
The correct option therefore has a domain as x > 0 and range as the set of all real numbers.
Learn more about finding the graphs of logarithmic functions here:
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