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.
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.