G4.4 Let $x$ and $y$ be real numbers and define the operation * as $x^{*} y=p x^{y}+q+1$. It is given that $1 * 2=869$ and $2 * 3=883$. If $2 * 9=d$, find $d$.
$\begin{array}{l}\left\{\begin{array}{c}p+q+1=869 \\ 8 p+q+1=883\end{array}\right. \\ \text { (2)-(1):7p=14 } \\ p=2, q=866 \\ \Rightarrow d=2 \times 2^{9}+866+1=1891\end{array}$