Question

Help solving this please. I am unsure how to do it?

Determine the domain of the following functions, write answer using interval notation.

P( x )=log2(3x-8)

Answer 1

we can only take logs of positive numbers
so 3x-8 > 0
3x > 8
x > 8/3

I will let you write it in the new-fangled notation.
In my time we used the above simple way of stating it.

Answer 2

the domain of log(u) is u>0, regardless of the base of the logs. So, you need

3x-8 >0
x > 8/3

or,

(8/3,∞)