Question

How do I get the domain for a logarithmic function?

Answer 1

what is the function?

Answer 2

\[f(x) = 3-2 \log_{4} [\frac{ x }{ 2 } -5]\]

Answer 3

You can only take log of a number greater than 0.
Therefore x/2 - 5 > 0
Solve for x and that will be the domain.

Answer 4

yeah but what about the whole \[3-2 \log_{4} \] ?

Answer 5

Domain means what are the values allowed for x.
All values of x are allowed as long as x/2 - 5 > 0
Solve the inequality and you will have your domain.
The rest of the terms does not matter.

Answer 6

Then what's the point of having them there? Other then to confuse you even more?