ln is an operation only for numbers greater than zero. Like this we know that (-x+3/2) must be greater than zero. Since 2 is a positive constant, we only need to make sure the term -x+3 is also positive and different than zero.
We can use this inequality to solve that problem:
[tex] - x + 3 > 0 \\ [/tex]
Put the 3 in the other side of the inequality like -3:
[tex] - x > - 3[/tex]
Now change the negative symbol, changing the inequality symbol as well
[tex]x < 3[/tex]
This means the domain of the function are all the numbers less than 3:
The answer is x<3
