Solution
= Solution
Write $q=A+Bx$ and $\ell=\log3$. <Orthogonality> of $x^2-q$ to $1$ and $x$ gives
$$
\begin{pmatrix}\ell&2\\2&4\end{pmatrix}\begin{pmatrix}A\\B\end{pmatrix}
=\begin{pmatrix}4\\26/3\end{pmatrix}.
$$
The <Gram matrix> is positive definite, with <determinant> $4(\ell-1)>0$, so the solution is unique. Solving yields
$$
\boxed{q(x)=-\frac1{3(\log3-1)}+\left(\frac{13}{6}+\frac1{6(\log3-1)}\right)x}.
$$