An article suggested using a↑b for ab and a↓b for loga(b) as a pedagogical approach drawn from Knuth’s up arrow and down arrow notation.
Advantages of this alternative notation include symmetry between exponents and logs, making the base of the logarithm more prominent, and a typographically linear representation.
The up and down arrow notation keeps expressions within a line, in contrast to conventional notation which extends above and below the line.
The article presents basic properties of logs and exponents using both conventional and up/down arrow notations.