Trying to solve this differential equation by separating variables. Where c is a constant and K is the carrying capacity. P is population

$\displaystyle \frac{{dP}}{{dt}} = c\ln \left( {\frac{K}{P}} \right)P$

I started with this

$\displaystyle

\begin{array}{l}

\frac{{dP}}{{dt}} = c\ln \left( {\frac{K}{P}} \right)P \\

dP = c\ln \left( {\frac{K}{P}} \right)P.dt \\

\frac{{dP}}{P} = c\left( {\ln (K) - \ln (P)} \right)dt \\

\end{array}

$

than I'm not sure if I can do this.

$\displaystyle

\begin{array}{l}

\frac{{dP}}{P} - c\ln (P) = c\ln K.dt \\

\frac{1}{P} - c\ln (P)dp = c\ln K.dt \\

\end{array}

$

and if it allowed than I'm lost at this point anyhow. I'm really not liking these, I seem lost in the process.