Correct : c

Explanation:
Let us simplify the given logarithmic equation step-by-step using standard logarithm rules.
1. Apply Logarithmic Properties:
The given equation is:
    ln((x + y) / 2) = 1/2 [ln(x) + ln(y)]

Using the log addition rule, ln(x) + ln(y) = ln(xy):
    ln((x + y) / 2) = 1/2 ln(xy)

Using the power rule, b · ln(a) = ln(ab):
    ln((x + y) / 2) = ln((xy)^1/2)

2. Remove the Natural Logarithm from Both Sides:
    (x + y) / 2 = √(xy)
    x + y = 2√(xy)

3. Square Both Sides to Eliminate the Radical:
    (x + y)² = (2√(xy))²
    x² + 2xy + y² = 4xy

Bring 4xy to the left side:
    x² - 2xy + y² = 0
    (x - y)² = 0
    x - y = 0 → x = y

4. Evaluate the Target Expression:
Since x = y, we substitute y for x (or vice versa) in the expression x/y + y/x:
    x/y + y/x = y/y + y/y = 1 + 1 = 2

5. Conclusion:
The value of the expression is exactly 2, making option (c) the correct choice.