  In this paper we determine which blow-ups $X$ of $\mathbb{P}^n$ at general
points are log Fano, that is, when there exists an effective
$\mathbb{Q}$-divisor $\Delta$ such that $-(K_X+\Delta)$ is ample and the pair
$(X,\Delta)$ is klt. For these blow-ups, we produce explicit boundary divisors
$\Delta$ making $X$ log Fano.
