Question 60
Find all real numbers $a$ such that the equation
$$
\log_{4 a x}(x-3 a)+\frac{1}{2} \log_{x-3 a} 4 a x=\frac{3}{2}
$$
has exactly two solutions.
$$
\log_{4 a x}(x-3 a)+\frac{1}{2} \log_{x-3 a} 4 a x=\frac{3}{2}
$$
has exactly two solutions.