I'm approaching for the first time GLS estimators.
Suppose that $\operatorname{Var}(u|x)=\sigma^2 h(x)$, where $h(x)$ is some function of the explanatory variables that determines the heteroscedasticity. Since variances must be positive, $h(x)>0$ for all possible values of the independent variables. Let's say, we don't know $h(x)$.
The book (Wooldridge, the introductory one) proposes the following way for modelling heteroscedasticity:
$$\operatorname{Var}(u|x)=\sigma^2 {\rm e}^{\delta_0 +\delta_1 x_1 + \cdots + \delta_k x_k}\tag 1$$
where $\delta_j$ are unknown parameters. Thus, $h(x)={\rm e}^{\delta_0 +\delta_1 x_1 + ... + \delta_k x_k}$
Then, the book says, under assumption $[1]$ I can write
$$u^2 =\sigma^2 ({\rm e}^{\delta_0 +\delta_1 x_1 + ... + \delta_k x_k}) \nu\tag 2$$
Where do equations $[2]$ and $[8.31]$ come from?