Question

Please help me find the domain and range of the logarithmic function

Answer 1

`\begin{gathered} \text{doma}\imaginaryI\text{n: }(0,\infty) \\ \text{range: }(-\infty,\infty) \end{gathered}`

Explanation:

We have the following logarithmic function:

`g\left(x\right)=\log _4\left(x\right)`

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:

`\begin{gathered} \text{domain: }\left(0,\:\infty\:\right)\text{ } \\ \text{range: }\left(-\infty\:,\:\infty\:\right) \end{gathered}`