Thinking about digit size is sort of fine for simplification / not turning off general audiences with equations, but a bit of a pain to think about if , e.g., the things you're comparing might be smaller than one.

What Lindelof says more precisely is that for any ε > 0 and any L-function L(s), there is a constant C_(ε,L) (depending only on ε and L, but crucially not on s) such that |L(s)| <= C_ε (1+|Im(s)|)^ε.