Find the minimal sufficient statistics for $y_i, i = 1, ..., n$ are independent Poisson with mean $\mu_i$ with $$\log(\mu_i) = \beta_o+\beta_1 x_i$$ where $x_i$'s are known predictors and $(\beta_0,\beta_1)$ are unknown parameters.
What I have done: $$\begin{align}X &\sim Pois(\log(\mu_i);x) \\ \implies L(\log(\mu_i);x) &= \prod_{i=1}^n \left(\frac{\log(\mu_i)^x\mu_i}{x!}\right) \\ &= \frac{\log(\mu_i)^{nx}\mu_i^n}{\prod_{i=1}^nx!} \end{align}$$
Where to go from here?