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

May 21, 2015

The domain of function $f \left(x\right)$ is the interval (4;+infty).

First you need to know that you can evaluate $\log \left(x\right)$ 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 $\log \left(x - 4\right)$, 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)