Show that a sequence can't be longer than $p+q-d$ when the product of every consecutive subsequence of length $p$ is $<1$ and $q$ products are $>1$

Question

This problem is from Engels Problem solving strategies. A p-product refers to a subsequence containing $p$ terms, that are picked consecutively and multiplied. I don't see what he is referring to when he says we can use logarithms here.