For positive non-zero real variables $p$ and $q$, if $$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3\ ,$$ then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is

Given the logarithmic equation:

Using logarithmic properties $\log a + \log b = \log(ab)$ and $n\log a = \log(a^n)$:

Taking antilogarithm on both sides:

Squaring both sides:

Subtracting $2p^2q^2$ from both sides:

Dividing both sides by $p^2q^2$:

Hence, the correct option is (A).