This equivoque depends on willfully mixing up the various meanings of the Greek word logos (λoγoς).
1. ratio, proportion (logarithm)
2. word (logophile, logorrhea)
3. speech (dialogue)
4. calculation (rabdology)
5. reasoning (logic)
For a full discussion see on the Greek word logos see
Using the meaning “word” for logos, we have
logarithm » logo + rhythm » word rhythm » poetry.
The actual etymology of logarithm is based on the meaning “proportion” for logos.
logarithm » log + arithm » proportional number.
Note: arithmos (αριθμoς) is Greek for number.
There are many fine examples of “mathematical” poetry. Two of my favorites are
Edna St.Vincent Millay
I have put together a small collection of sites with “mathematical” poetry here.