Answer:

No, [tex]\log_{3} (A+1)[/tex] can't be rational.

Step-by-step explanation:

Let's take an example.

Let A be 27.

So, [tex]\log_{3} (27)[/tex] = [tex]3[/tex]

But, A+1 = 28 & as we all know, 3 has no rational power for the value 28.

So, [tex]\log_{3} (A+1)[/tex] can't be rational for any value of A.

Step-by-step explanation:

Let's take an example.

Let A be 27.

So, \log_{3} (27)log3(27) = 33

But, A+1 = 28 & as we all know, 3 has no rational power for the value 28.

So, \log_{3} (A+1)log3(A+1) can't be rational for any value of A.