3Log 2 + 1/2 log 81 as a logarithm of a single number.

The given expression is 3Log 2 + 1/2 log 81.

Step 1: Apply the power rule of logarithms, which states that logb(m^n) = n*logb(m).

This gives us: Log(2^3) + Log(81^(1/2)).

Step 2: Simplify the exponents.

This gives us: Log(8) + Log(9).

Step 3: Apply the product rule of logarithms, which states that logb(m*n) = logb(m) + logb(n).

This gives us: Log(8*9).

Step 4: Simplify the multiplication.

This gives us: Log(72).

So, 3Log 2 + 1/2 log 81 simplifies to Log(72).