determine the domain of f(x) =log2(x=3)?

I am going to assume that you, like me :D, occasionally make a typo and, with the minus sign right next to the equal sign, that this problem is really:

f(x) = log(base2) (x-3)

Since you cannot take the logarithm of 0 or a negative number, (x - 3) >0

Adding 3 to both sides of that inequality you get x > 3.

The domain, in set theoretic notation, is { x | x is real and x > 3 }

In interval notation it is (3, ∞)

___________________

If you care, the range is all of the real numbers.

Good luck in your course :D

.

.