Question 1196707
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{{{log(2,(x-2))+log(2,(x+1))=2}}}<br>
A sum of logs is the log of the product:<br>
{{{log(2,(x^2-x-2))=2}}}<br>
{{{x^2-x-2=2^2=4}}}
{{{x^2-x-6=0}}}
{{{(x-3)(x+2)=0}}}
{{{x=3}}} or {{{x=-2}}}<br>
But x = -2 is invalid because we would have to take the logarithm of a negative number.<br>
ANSWER: x=3<br>
CHECK: {{{log(2,(3-2))+log(2,(3+1))=log(2,(1))+log(2,(4))=0+2=2}}}<br>