We have calculated the following logs:
1 = 0
2 = 0.301
3 = 0.477
4 = 2 * log 2 = 0.602
5 = 1 - log 2 = 0.699
6 = log 2 + log 3 = 0.778
7 = 0.845
8 = 3 * log 2 = 0.903
9 = 2 * log 3 = 0.954
10 = 1
Next number is eleven.
How to calculate log 11? Here is a way to do this.
We can take the geometric mean of 10 and 12.
The geometric mean between 10 and 12 is sqrt(10 * 12) = sqrt(120).
However; to be precise, for log 11 we need log(sqrt(121)).
120 is close to 121 though. We need a small correction to be precise (0.833%).
log 120 = log (10*4*3) = log 10 + log 4 + log 3= 1 + 0.477 + 0.602 = 2.079
Now we add the small correction.
We calculated log (120) and we need log(121).
1/120 = 0.833… %
If the log of 1% = 0.0043, then 0.833% = 0.0043 *0.833 = 0.00358.
2.079 + 0.00358 = 2.08258.
2.08258 / 2 = 1.04129
log 11 = 1.04139