Question 5
For each ordered pair of real numbers $(x, y)$ satisfying $$
\begin{aligned} &\log_2(2x + y) \\ &= \log_4(x^2 + xy + 7y^2), \end{aligned}
$$ there is a real number $K$ such that $$
\begin{aligned} &\log_3(3x + y) \\ &= \log_9(3x^2 + 4xy + Ky^2). \end{aligned}
$$ Find the product of all possible values of $K.$
\begin{aligned} &\log_2(2x + y) \\ &= \log_4(x^2 + xy + 7y^2), \end{aligned}
$$ there is a real number $K$ such that $$
\begin{aligned} &\log_3(3x + y) \\ &= \log_9(3x^2 + 4xy + Ky^2). \end{aligned}
$$ Find the product of all possible values of $K.$