log 10=1,
log 2= 0.3010, and
log 3= 0.4771.
From these values, we can find many other log values.
log 5 = log 10 - log 2 = 0.699
log 0.5 = 0–log 2 = -0.301
log 1.5 = log 3 - log 2 = 0.1761
log 2.5 = log 5 - log 2 = 0.398
To find log of any number y:
Express y as (10^m)*(2^n)*(3^p)*(1+x).
Approximate log(1+x) as
(0.4343)*(x-x^2/2+x^3/3)
Or 0.4353*(x-x^2/2)
log y =
m + 0.3010*n + 0.4771*p + (0.4353)*(x-x^2/2+x^3/3)
To find log 13
13=2^2*3*(1+1/12)
log 13
= 2*0.3010 + 0.4771 + (0.4353)*(1/12 - 1/288+1/5184)
= 0.6020 + 0.4771 + 0.034847
= 1.1139