$$x'\ =\ r\cdot x\cdot \ln\left(\frac{ {K} }{x}\right)$$
Analyze fixed points and their stability depending on the parameters. I found one fixed point $x = K$ and the stability of this point. If $r < 0 \implies$ $x=K$ is unstable, if $r > 0\implies$ $x=K$ is stable.
And I know that second fixed point should be $x=0$, but I'm not sure how to determine it's stability. If someone could help me I would be grateful.