Approximation for $\prod\limits_{r<p\le P}\left( 1-\frac rp\right)^{-1}$

Question

Is there an approximation for $\prod\limits_{r<p\le P}\left( 1-\frac rp\right)^{-1}$ when $r$ is fix and greater than $1$ and $p$ is prime

For example if $r=1$ then the above is approximately $\log(P)$

Can we say something like $\log(P)^r$ ?