To begin note that 210 = 1024 which is very close to 1000 = 103.
210 ≈ 103
10 log 2 ≈ 3
log 2 ≈ 3/10 = 12/40
For 3, note that 34 = 81 which is very close to 80.
34 ≈ 80 = 10*23
4 log 3 ≈ 1 + 3 log2 ≈ 76/40
log 3 ≈ 19/40
Since 4 = 22, log 4 = 2 log 2 ≈ 2*12/40 = 24/40
Since 5 = 10/2, log 5 = log 10 - log 2 ≈ 1 - 12/40 = 28/40
Since 6 = 2*3, log 6 = log 2 + log 3 ≈ 12/40 + 19/40 = 31/40
For 7, note 72 = 49 which is close to 50 = 100/2
log 72 = log 100/2
2 log 7 = 2 - log 2 ≈ 2 - 12/40 = 68/40
log 7 ≈ 34/40,
see the comments for an argument about why 33/40 is also pretty good.
Since 8 = 23, log 8 = 3 log 2 ≈ 3*12/40=36/40
Since 9 = 33, log 9 = 2 log 3 ≈ 2*19/40=38/40 |
