Comment by cperciva

My approach: ln(19683) ~ ln(20000) = ln(20) + 3 ln(10) ~ 3 + 3*2.3 = 9.9. 3.3 = 1.0 + 2.3 ~ ln(e) + ln(10).

My mental landmarks are ln(2), ln(e), and ln(10), roughly 0.7, 1.0, and 2.3 respectively.