A link between zeroth powers and the logarithm function is such a simple idea but potentially fruitful. Exponentials and logarithms often translate between addi

A link between zeroth powers and the logarithm function is such a simple idea but potentially fruitful. Exponentials and logarithms often translate between additive groups and multiplicative groups. Maybe there are interesting isomorphisms where the logarithm can be generalized as a zeroth power.