Question 150019
Logarithm rules
{{{log((A*B))=log(A)+log(B)}}}
{{{log((A)^N)=Nlog(A)}}}
{{{log((A/B))=log(A)-log(B)}}}
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.
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{{{2*log(2,x)-log(2,(x+4))=log(2,2)}}}
{{{log(2,x^2)-log(2,(x+4))=log(2,2)}}}
{{{log(2,(x^2/(x+4)))=log(2,2)}}}
Take the inverse log of both sides.
{{{x^2/(x+4)=2}}}
{{{x^2=2(x+4)}}}
{{{x^2=2x+8}}}
{{{x^2-2x-8=0}}}
{{{x-4)(x+2)=0}}}
First solution 
{{{x-4=0}}}
{{{x=4}}}
Second solution 
{{{x+2=0}}}
{{{x=-2}}}
Second solution is not allowed since {{{log(2,(-2))}}} is not defined.
{{{highlight(x=4)}}}