Question 1206411
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Starting expression is

    {{{log(6, (216^x/1296^x))}}} . {{{log(x,6)}}}.


First factor is 

    {{{log(6, (216^x/1296^x))}}} = {{{log(6,(1/6^x))}}} = -x.


Second factor is 

    {{{log(x,6)}}} = {{{1/log(6,x)}}}.


The product of two factors is  -{{{x/log(6,x)}}}.


<U>ANSWER</U>.  The simplified expression is  -{{{x/log(6,x)}}}.
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Solved.