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According to Wikipedia and other sources, the question whether $L=P$ is an open problem, and of course everyone is familiar with the problem of whether $P=NP$. However, I found absolutely no information online regarding a possible equality between $L$ and $NP$.

Such an equality doesn't directly violate the space-hierarchy theorem or the time-hierarchy theorem, and so I don't have any idea how to disprove it.

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The question whether $L = NP$ is an open problem [1], so yes, it is possible. However, it is considered unlikely, or in other words, most believe that $L \subsetneq P \subsetneq NP \subsetneq PSPACE$, but we only know that $L \subsetneq PSPACE$ [2, 3].

References:

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