  We continue to study the logarithmic prismatic cohomology defined by the
first author, and complete the proof of the de Rham comparison and \'etale
comparison generalizing those of Bhatt and Scholze. We prove these comparisons
for a derived version of logarithmic prismatic cohomology, and, along the way,
we construct a suitable Nygaard filtration and explain a relation between
$F$-crystals and $\mathbb{Z}_p$-local systems in the logarithmic setting.
