Question 43
Find all values of the real parameter $a$ such that the equation
$$
\log_{a x}\left(3^{x}+4^{x}\right)=\log_{(a x)^{2}}\left(7^{2}\left(4^{x}-3^{x}\right)\right)+\log_{(a x)^{3}} 8^{x-1}
$$
has a solution.
$$
\log_{a x}\left(3^{x}+4^{x}\right)=\log_{(a x)^{2}}\left(7^{2}\left(4^{x}-3^{x}\right)\right)+\log_{(a x)^{3}} 8^{x-1}
$$
has a solution.