69 rule

on the other hand ln(67) = 4.20469… there certainly is some merit to the new meme number

I never knew this fun fact ! I’ll try to use it with my students, and see if I this gets me more attention when I give them the trick to compute powers of 2 in your head (2¹⁰ =~ 10³, which leads to ln(10³) =~ 10*ln(2) ).

For anyone wondering, the trick is : Powers of 2 below 10 are easy enough to remember or just compute in your head. So if you want to approximate 2^x, write it as (2^10*a)*(2^b), with a=x//10 (integer division) and b=x%10 (modulo). b will be 9 or less, so 2^b is easy to compute, and 2^10*a = (2¹⁰)^a =~ 1000^a is also easy to compute.

For instance, 2³² = (2³⁰)(2²). Since 2³⁰=~1000³ ; and 2²=4, then 2³² =~ 4(1000)^3 = 4 billion. Once you get used to it, you’ll be able to say that 2⁶⁴ is approx 16 billion billions in no time ! :)

‘ln’? My brother in Euler, that’s jist log. We aren’t engineers [derogatory].

Nice