Solve the following equation for $$x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$$
Answer
$${a^{{\raise0.5ex\hbox{$\scriptstyle { - 1}$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}},\,\,{a^{{\raise0.5ex\hbox{$\scriptstyle { - 4}$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 3$}}}}$$
