Question 375867
{{{log((2x+3))+log((x-2))=2log((x))}}}
{{{log((2x+3)(x-2))=log((x^2))}}}
{{{(2x+3)(x-2)=x^2}}}
{{{2x^2-x-6=x^2}}}
{{{x^2-x-6=0}}}
{{{(x-3)(x+2)=0}}}
Two solutions:
{{{x-3=0}}}
{{{x=3}}}
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{{{x+2=0}}}
{{{x=-2}}}
Verify the solutions.

{{{log((2x+3))+log((x-2))=2log((x))}}}
{{{log((2(3)+3))+log((3-2))=2log((3))}}}
{{{log((9))+log((1))=2log((3))}}}
{{{log((9))=log((9))}}}
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{{{log((2x+3))+log((x-2))=2log((x))}}}
{{{log((2(-2)+3))+log((-2-2))=2log((-2))}}}
This solution is not allowed since the log function requires a positive argument.
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{{{highlight(x=3)}}}