how to find log

It seems as you are facing problem in finding log values from the log table..

Let us understand log calculation, with the help of an example.

Suppose we have to find log of 3.352 x 10¹¹.

Taking log,

log(3.352 x 10¹¹) = log (3.352) + log(10¹¹)

log(3.352 x 10¹¹) = log(3.352) + 11 log(10)

log(3.352 x 10¹¹) = 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 10¹¹) = 11+0.5253 = 11.5253

Let us now, take antilog of 11.5253.

The digits before the decimal becomes the mantissa.

antilog(11.5253) = antilog(0.5253) x 10¹¹

To find the value of antilog(0.5253), we will look for the value in 0.52^th row, 5^th column, which is 3350. To this value add the mean difference of 3^rd column, in the same row, in the antilog table.

3350+2=3352

Therefore, antilog(0.5253)=3.352.

So, antilog(11.5253) = 3.352 x 10¹¹.

There are three standard laws of logarithms.

(i) Product Law

In general,

(ii) Quotient Law

(iii) Power Law

Hope, its clear now.

Enjoy learning!!