To find the logarithm:
- We always express the number in the standard form using characteristic and mantissa.
- The standard form of a number a using characteristic and mantissa is a = m x 10c , where c and m are the characteristic and mantissa.
- If a = m x 10c then log a = c + log m. To find the value of log m, we use the log table. Also,
Let us understand log calculation, with the help of an example.
Suppose we have to find log of 3.352 x 10 11 .
log(3.352 x 10 11 ) = log (3.352) + log(10 11 )
log(3.352 x 10 11 ) = log(3.352) + 11 log(10)
log(3.352 x 10 11 ) = log(3.352) + 11
To find log(3.352), we will look for the value in 33 th row, 5 th column, which is 5250. To this we add the mean difference of the 2 nd column, in the same row, in the log table.
5250 + 3 = 5253.
Now, log(3.352) = 0.5253
So, log(3.352 x 10 11 ) = 11+0.5253 = 11.5253