Succinctly: lim_(n→∞) bits_needed(3ⁿ) / n = lim_(n→∞) ⌈log2(3ⁿ)⌉ / n = lim_(n→∞) ⌈n log2(3)⌉ / n = log2(3) = log(3) / log(2) where bits_need

Succinctly: lim_(n→∞) bits_needed(3ⁿ) / n = lim_(n→∞) ⌈log2(3ⁿ)⌉ / n = lim_(n→∞) ⌈n log2(3)⌉ / n = log2(3) = log(3) / log(2) where bits_needed(m) is the minimum number of bits needed to encode m distinct values.