What is the domain of the function

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:

Put the 3 in the other side of the inequality like -3:

Now change the negative symbol, changing the inequality symbol as well

This means the domain of the function are all the numbers less than 3:

The answer is x<3