Picking parameters such that the limit goes towards 1.

Question

I have the below term and would like to pick the parameter $p$, such that the limit as $x\to\infty$ goes towards 1. We know that $k > 0$

$\lim_{x\to\infty}\log^3(x) + \log(x)x^{p} - \log^2(x)x^k \to 1$.

I have tried factoring $\log^2(x)$ out and then using L'Hospital after seeing that we get something like , $\infty - \infty$, but to no success.

Are there any smarter ways of going about this?

Thanks in advance