How do you solve Ln(x+1)-ln(x-2)=lnx^2?

Jul 17, 2016

$x \approx 2.54682$

Explanation:

$\implies \ln \left(\frac{x + 1}{x - 2}\right) = \ln \left({x}^{2}\right)$
$\implies \frac{x + 1}{x - 2} = {x}^{2}$
$\implies x + 1 = {x}^{2} \left(x - 2\right)$
$\implies x + 1 = {x}^{3} - 2 {x}^{2}$
$\implies {x}^{3} - 2 {x}^{2} - x - 1 = 0$
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$x \approx 2.54682$