If lim n → ∞ x n log e x = 0 then log x 12 =

Given,

$\underset{n\to \infty }{\lim }{x}^n{\log }_{e}x=0$

We know that when $n\to \infty$, $x^n\to 0$ when $x\in \left(0,1\right)$

So, $\underset{n\to \infty }{\lim }{x}^n{\log }_{e}x=0$ is only possible when $x\in \left(0,1\right)$

Then ${\log }_{x}12$ will be negative as base belongs to $\left(0,1\right)$.