Compute logarithms in your head
Käännös: [ Google ]
Kategoriat: [ Tiede ]
Let's consider base 10 logarithms and the basic equality
log(a×b) = log(a) + log(b)Rounding to two places after the decimal separator, we also start with
log(2) = 0.30and
log(10) = 1Therefore, we have
log(4) = 2⋅log(2) = 0.60and
log(8) = 3⋅log(2) = 0.90Also,
log(10) = log(2) + log(5) = 1therefore
log(5) = 0.70Then a bit more approximation: 81 ≈ 80, therefore
2⋅log(9) ≈ log(10) + log(8)This gives us
log(9) ≈ 0.95and
log(3) = log(9)/2 = 0.48as well as
log(6) = log(2) + log(3) = 0.78In the same way, 50 ≈ 49, therefore
log(5) + log(10) ≈ 2⋅log(7)in other words,
log(7) ≈ 0.85
With more approximations, one will find the logs of more prime numbers without the need for a calculator.
[ Postattu 2. joulukuuta 2014 klo 00.02 | ei kommenttia | kestävä linkki ]
