log-linearize a forward looking variable (P/D) with recursive expression

I can solve the model in dynare but I need your help with the following problem: How does one derive a log-linearized expression for a forward-looking variable around the steady-state? For example, the price dividend ratio can be defined as

$frac{P_t}{D_t} = E_t [M_{t,t+1}frac{D_{t+1}}{D_t}(1+
frac{P_{t+1}}{D_{t+1}})]$

The goal is to derive the relation between $frac{P_{t+1}}{D_{t+}}$ and shocks / state variables at $t+1$, assuming that at $t$ the system is in steady state so $frac{P_t}{D_t}$ is the steady state value C.

If we ignore the expectation and log-linearize it, I get

$log C = m_{t,t+1} + Delta D_{t+1} + log(1+frac{P_{t+1}}{D_{t+1}})$

and clearly one can solve $frac{P_{t+1}}{D_{t+1}}$ analytically (assuming that $m$ and $Delta D$ are known functions of shocks/state variables).

But, isn’t ignoring expectation imposing that the equality hold state by state, instead of on average?

Please advise, thanks!