ANSWER:
[tex]\begin{gathered} \text{doma}\imaginaryI\text{n: }(0,\infty) \\ \text{range: }(-\infty,\infty) \end{gathered}[/tex]
STEP-BY-STEP EXPLANATION:
We have the following logarithmic function:
[tex]g\left(x\right)=\log _4\left(x\right)[/tex]
The domain is all the input values of the function, in this case it would be the range of values that x can take that has a real image.
The range is all the output values of the function, in this case it is the interval of values that y would take.
We know that 0 and negative numbers cannot be in logarithms, because there is no real image.
Therefore, the domain and range would be:
[tex]\begin{gathered} \text{domain: }\left(0,\:\infty\:\right)\text{ } \\ \text{range: }\left(-\infty\:,\:\infty\:\right) \end{gathered}[/tex]
