Estimate logarithm quickly

[Albert Chan]

This is an amazing formula, for estimating ln(n) to 5 sig. digits, n = [1/√2, √2]
(again, from "Dead Reckoning", p. 132)

ln(n) ≈ 6*(n-1) / (4*√n + n+1)

use 1/ln(10) = 0.4342945 ... to scale back for log10.

Example, for log10(3):

3^2 = 0.9e1

log10(0.9) ≈ 0.4343 * 6 * -.1 / (4*√.9 + 1.9) ≈ -0.04576
log10(3) ≈ (-0.04576 + 1) / 2 = 0.47712


Or, scale by 2^k factor, log10(2) ≈ 0.30103

3 * 4 = 1.2e1

log10(1.2) = 0.4343 * 6*.2/(4*√1.2 + 2.2) ≈ 0.07918
log10(3) ≈ 0.07918 + 1 - 2*0.30103 = 0.47712