Question 805114
<pre>
{{{2log (3,x)-log(3,(x-4))=2+log(3,2)  }}}

Isolate the logs on whichever side will cause the most logs to be
positive:


                     {{{-2=log (3,2)+log(3,(x-4))-2log (3,x)}}}
                     {{{-2=log (3,2(x-4))-2log (3,x)}}}
                     {{{-2=log (3,2(x-4))-log (3,x^2)}}}
                     {{{-2=log(3,2(x-4)/x^2)}}}
                     {{{3^(-2)=2(x-4)/x^2}}}
                     {{{1/3^2=2(x-4)/x^2}}}
                     {{{1/9=2(x-4)/x^2}}}
                     {{{x^2=18(x-4)}}}
                     {{{x^2=18x-72}}}
                     {{{x^2-18x+72=0}}}
                     {{{(x-6)(x-12)=0}}}
                     x-6=0;  x-12=0
                       x=6;     x=12

Neither answer causes the original problem to take the
log of a negative number.  So those are the solutions.

If you have any questions, ask them in the thank-you note 
and I'll get back to you.

Edwin</pre>