Question

How do you find the domain of `y=log_3 (x-2)`?

Answer 1

The domain is: `D=(2;+oo)`. See explanation.

Explanation:

The domain of a function is the biggest subset of real numbers set for which the value of function is defined.

Here we have to assume that `x-2>0` because logarythm is only defined for positive numbers. So we get:

`x-2>0`

`x>2`

If we write this set as an interval we get: `x in (2;+oo)`