Question 292991
{{{log(2,(x))+log(2,(x-6))=4}}}
{{{log(2,(x(x-6)))=4}}}
{{{x(x-6)=2^4=16}}}
{{{x^2-6x-16=0}}}
Factor,
{{{(x-8)(x+2)=0}}}
Two solutions:
{{{x-8=0}}}
{{{x=8}}}
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{{{x+2=0}}}
{{{x=-2}}}
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Verify the solutions.
{{{log(2,(x))+log(2,(x-6))=4}}}
{{{log(2,(8))+log(2,(8-6))=4}}}
{{{3+log(2,(2))=4}}}
{{{3+1=4}}}
{{{4=4}}}
True, it's a good solution.
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{{{log(2,(-2))+log(2,(-2-6))=4}}}
{{{log(2,(-2))+log(2,(-8))=4}}}
Log arguments must be positive. 
This solution is not valid. 
Only one solution, {{{highlight_green(x=8)}}}