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Tuesday, December 2nd, 2014

Compute logarithms in your head

Categories: [ Science ]

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) = 0.30
and
log(10) = 1
Therefore, we have
log(4) = 2⋅log(2) = 0.60
and
log(8) = 3⋅log(2) = 0.90
Also,
log(10) = log(2) + log(5) = 1
therefore
log(5) = 0.70
Then a bit more approximation: 81 ≈ 80, therefore
2⋅log(9) ≈ log(10) + log(8)
This gives us
log(9) ≈ 0.95
and
log(3) = log(9)/2 = 0.48
as well as
log(6) = log(2) + log(3) = 0.78
In 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.

[ Posted on December 2nd, 2014 at 00:02 | no comment | ]

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