Question 1042897
{{{log((x-1)^2)-log((x+2))=-log((8))}}}
{{{log((x-1)^2/(x+2))=log((1/8))}}}
{{{(x-1)^2/(x+2)=1/8}}}
{{{8(x-1)^2=x+2}}}
{{{8x^2-17x+6=0}}}
Complete the square,
{{{8(x^2-(17/8)x)+6=0}}}
{{{8(x^2-(17/8)x+(17/16)^2)+6=8(17/16)^2}}}
{{{8(x-17/16)^2=8(17/16)^2-6}}}
{{{8(x-17/16)^2=8(289/256)^2-6(256/256)}}}
{{{8(x-17/16)^2=776/256)}}}
{{{(x-17/16)^2=97/256)}}}
{{{x-17/16=0 +- sqrt(97)/16}}}
{{{x=17/16 +- sqrt(97)/16}}}
{{{x=(17 +- sqrt(97))/16}}}
However the negative value would lead to a negative argument in the log function so only the positive solution works.
{{{x=(17+sqrt(97))/16}}}