Is it possible that $L=NP$?
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:


[1] Taking Passes at NP Versus L — Gödel's Lost Letter and P=NP
[2] L/P/PSpace vs P/NP — cstheory.stackexchange.com
[3] If P=NP, then is L=NL? — cs.stackexchange.com