Single-digit multiplication is just a mapping of a set of 55 (distinct) values to a set of 37 (distinct) values

multiply_digits.js

const multipliers = new Map();
const multiplications = new Set();

for (let i = 0; i < 10; i++) {
    for (let j = i; j < 10; j++) {
        const res = i * j;
        multiplications.add(res);
        multipliers.set(
            i.toString() + j.toString(),
            res,
        );

        const logRes = Math.round(
            Math.pow(10, Math.log10(i) + Math.log10(j))
        );
        console.assert(res === logRes);
    }
}

See also:

Irish logarithm

Percy Ludgate’s Logarithmic Indexes