Consider degree \(1\) genus \(0\) stable maps with one marked point to \(\mathbb P^2\) endowed with divisorial log structure coming from \(D \subset \mathbb P^2\) a smooth divisor. An ordinary stable map \(f:\mathbb P^1\to \mathbb P^2\) lifts to a log stable map if and only if the marked point hits the divisor \(D\), so we should be able to realize the moduli space of stable log maps as a closed subscheme of \(\overline{M}_{0,1}(\mathbb P^2, 1)\) corresponding to the fiber of \(D\) over the evaluation map \(\ev:\overline{M}_{0,1}(\mathbb P^2, 1) \to \mathbb P^2\), i.e.