What is the value of log13

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