How do you solve $ln(x+1)-ln(x-2) = ln x$ ?

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Answer 1 · 2018-04-03T03:16:58

$x=3.30$

$In(x+1)-In(x-2)=Inx$
$In(x+1)/(x-2)=Inx$
$(x+1)/(x-2)=x$
$x+1=x(x-2)$
$x+1=x^2-2x$
$x^2-3x-1=0$

Using quadratic formula,
$x=(3+-sqrt(9+4))/2$
$x=(3+sqrt13)/2 or (3-sqrt13)/2$
$x=3.30 or -0.302$

BUT you can't log a NEGATIVE number so $x=-0.302$

Therefore, $x=3.30$ is the only answer

How do you solve ln(x+1)-ln(x-2) = ln xln(x+1)-ln(x-2) = ln x?