To solve this expression:

8(1/3 + log₂(3) / log₂(log₃(81))

First, simplify the logarithmic terms using the change of base formula:

log₃(81) = log₂(81) / log₂(3)
= log₂(3^4) / log₂(3)
= 4 log₂(3) / log₂(3)
= 4

Therefore, we have:

8(1/3 + log₂(3) / 4)

Now simplify further:

8(1/3 + log₂(3) / 4) = 8(1/3 + 1/4) = 8(4/12 + 3/12) = 8(7/12) = 56/3

So, the value of the expression is 56/3.