Question 1083496
{{{log(3, (4x))+log(3,(x-4)) =2}}}


{{{log((4x))/log((3))+log((x-4))/log((3)) =2}}}


{{{(log((4x))+log((x-4)))/log((3)) =2}}}


{{{log(4x(x-4))/log((3)) =2}}}


{{{log(4x(x-4)) =2log((3))}}}


{{{log(4x(x-4)) =log((3^2))}}}.......if log same, we have


{{{4x(x-4) =9}}}


{{{4x^2-16x =9}}}


{{{4x^2-16x -9=0}}}


{{{4x^2+2x-18x -9=0}}}


{{{(4x^2+2x)-(18x +9)=0}}}


{{{2x(2x+1)-9(2x +1)=0}}}


{{{(2x - 9)(2x + 1) = 0}}}

solutions:

if {{{(2x - 9) = 0}}}->{{{2x=9}}}->{{{x=9/2}}} or {{{x=4.5}}}

if {{{(2x + 1) = 0}}}->{{{2x=-1}}}->{{{x=-1/2}}} -> since log, disregard negative solution

so, your solution is: {{{x=9/2}}} or {{{x=4.5}}}