Answer
$-1\pm\sqrt{1+e^3}$
Work Step by Step
We know that $x\log_ab=\log_ab^x$ and that $\log_ab+\log_ac=\log_a(bc)$
Hence here $\ln x+\ln (x+2)=3\\\ln(x(x+2))=3\\e^3=x(x+2)$
Then using the quadratic formula we get: $x=\frac{-2\pm\sqrt{(-2)^2-4(1)(-e^3)}}{2(1)}=\frac{-2\pm\sqrt{4+4e^3}}{2}=-1\pm\sqrt{1+e^3}$
