Question

How do you find the domain of `f(x)=(log[x-4])/(log[3])`?

Answer 1

The domain of function `f(x)` is the interval `(4;+infty)`.

First you need to know that you can evaluate `log(x)` only when `x` is positive (`x>0`) and equals `0` only when `x=1`.

So, in our denominator we don't any problems, `3` is a positive number different that `1` so we get a nonzero denominator.

Our numerator consists of `log(x-4)`, which can be `0` but this doesn't concern us particularly. The number inside, `x-4`, must be positive, though. So:

`x-4>0`
`x>4`
`x in (4;+infty)`