Question 574529
That answer makes sense because
{{{log(2x,216)=x}}} --> {{{log(2x,6^3)=x}}} --> {{{log(2x,(2*3)^3)=x}}}
Maybe you were expected to graph and check. Maybe you would transform the equation like this:
{{{log(2x,6^3)=x}}} --> {{{3log(2x,6)=x}}} --> {{{3log(3,6)/log(3,2x)=x}}}
At this point, you would realize that the graphs of the functions
{{{y=3log(3,6)/log(3,2x)}}} and {{{y=x}}} look like this, intersecting at just ore point that appears to be (3,3)
{{{graph(300,300,-1,5,-6,12,3log(3,6)/log(3,2x),x)}}}
and making a further transformation, you would realize, and easily prove that x=3 is indeed the answer
{{{3log(3,(2*3))/log(3,(2*x))=x}}} --> {{{3(log(3,2)+1)=x(log(3,2)+log(3,x))}}}