[rwqjdczw] Ten Common logarithms

By memorizing a table of logarithms base 10, one can multiply by using addition. A log table could be just as easy (or hard) to memorize as a standard digit multiplication table, but be much more useful because the information is more concentrated in a range where it matters (values 1 through about 3). How big a table should one memorize? How many significant digits for each log? How should one round? I don't have a rigorous way of answering these questions. We try to keep the relative error low, but also keep entropy low. Here is a simple table, also giving the boundaries between each log. The plus or minus suffix gives the direction of the exact boundary, so a number at the given boundary should be rounded the opposite direction.

0 =	log	1
		1.1+
0.1 =	log	1.26
		1.4+
0.2 =	log	1.6
		1.8-
0.3 =	log	2
		2.2+
0.4 =	log	2.5
		2.8+
0.5 =	log	3.2
		3.5+
0.6 =	log	4
		4.5-
0.7 =	log	5
		5.6+
0.8 =	log	6.3
		7+
0.9 =	log	8
		9-
1 =	log	10

For example 2.8 < pi < 3.5, so log(pi)=0.5 ; 2.2 < e < 2.8, so log(e)=0.4 ; log (pi*e) = 0.4 + 0.5 = 0.9 = log (8), or pi*e = 8. Actual value 8.539734223 .