  We study the following Choquard type equation in the whole plane $(C) -\Delta
u+V(x)u=(I_2\ast F(x,u))f(x,u),x\in\mathbb{R}^2$ where $I_2$ is the Newton
logarithmic kernel, $V$ is a bounded Schr\"odinger potential and the
nonlinearity $f(x,u)$, whose primitive in $u$ vanishing at zero is $F(x,u)$,
exhibits the highest possible growth which is of exponential type. The
competition between the logarithmic kernel and the exponential nonlinearity
demands for new tools. A proper function space setting is provided by a new
weighted version of the Pohozaev--Trudinger inequality which enables us to
prove the existence of variational, in particular finite energy solutions to
$(C)$.
