To solve the given equation log {(ab)/4} = 1/2 (log a log b), we need to simplify it step by step.

Step 1: Simplify the equation
Using the properties of logarithms, we can rewrite the equation as:
log(ab) - log(4) = 1/2 (log a + log b)

Step 2: Simplify further
Using the property log(ab) = log a + log b, the equation becomes:
log a + log b - log 4 = 1/2 (log a + log b)

Step 3: Combine like terms
Simplifying the equation, we have:
log a - 1/2 log a + log b - 1/2 log b = log 4

Step 4: Combine coefficients
Combining the coefficients of log a and log b, we get:
1/2 log a + 1/2 log b = log 4

Step 5: Use the property of logarithms
Using the property log a + log b = log(ab), the equation becomes:
log (√(ab)) = log 4

Step 6: Remove the logarithm
Since the logarithms on both sides are equal, their arguments must be equal as well:
√(ab) = 4

Step 7: Solve for a/b
To find the value of a/b, we need to isolate a and b separately.
Squaring both sides of the equation, we get:
ab = 16

Dividing both sides of the equation by b, we have:
a = 16/b

Step 8: Substitute the value of a into a/b
Substituting the value of a into a/b, we get:
(16/b)/b = 16/b^2

Step 9: Simplify the expression b/aa
To simplify the expression b/aa, we divide b by aa:
b/aa = b/(a^2)

So, the answer is 16/b^2 or option (c) 16.