CBSE Class 12-science Answered

The logarithm of a number has two parts the first of which is the exponent of 10, called the characteristic, and the second part is a decimal called the mantissa which is read from the log tables. The characteristic can be positive or negative. The negative characteristic is written with a bar above the number. The mantissa is always a positive decimal less than 1.

How to find log:

To look up a logarithm of say, 15.27, you would First work out the characteristic, in this case it is 1 Run your index finger down the left-hand column until it reaches 15 Now move it right until it is on column 2 (it should be over 1818) Using another finger, find the difference on column 7 of the differences (20) Add the difference.

So the logarithm of 15.27 is 1.1818 + 0.0020 = 1.1838

Antilog of x is equal to 10^x

For example find the antilog of 2.6992

The number before the decimal point is 2, so the decimal point will be after the first 3 digits.

From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.

Now place a decimal point after the first 3 digits and you get the number 500.2

Thus antilog 2.6992 = 500.2

Examples of multiplication and division by using logs:

  Answered by | 16 Apr, 2013, 10:49: AM