Writing Systems of the World 3, Exercise 3: why logographies are large

From Chapter 1: a logographic symbol stands for a unit of meaning (a word or
morpheme), an alphabetic symbol for roughly a phoneme.

A language has a few dozen phonemes but thousands of morphemes. A system that
gives each morpheme its own symbol therefore needs thousands of symbols (the
article: roughly 3,500 to 5,000 characters for frequent vocabulary), while a
system that records only phonemes needs fewer than 100.

The trade-off (my summary): the logographic system is large to learn but ties
each symbol directly to meaning; the alphabetic one is small to learn but
needs rules to turn letters into sounds and then into words.