Use of Logarithms in Multiplication

Solution. In the calculator, the negative characteristic and positive mantissa

were combined by algebraic addition to form the single negative number. To change a

negative logarithm to the correct form, add the next highest positive whole number

above the characteristic's (absolute value) to the negative log. This operation will yield

the positive mantissa.

3 - 2.5017 = 0.4983

Use the additive inverse (negative form in this instance) of the whole number that was

added as the characteristic of the corrected logarithm, and indicate its sign with a bar

over the number.

3.4983

Rewrite 3.4983 as 0.4983 - 3. This puts the logarithm in the form of an exponential

expression. Take the antilog of both numbers.

Antilog 0.4983 X antilog (-3)

NOTE:

The two antilog expressions are multiplied together since they represent

numbers, not logs (refer to the Rules of Exponentiation in paragraph 1-20).

The antilog of 0.4983 = 3.15

The antilog of -3 = 10-3

Therefore, the antilog of -2.5017 = 3.15 X 10-3

1-39. USE OF LOGARITHMS IN MULTIPLICATION

To multiply two or more numbers together, the logarithm of each number is found

and the logarithms of each are added together. The antilogarithm of the sum of the

logarithms is then taken to give the product of the multiplication.

Example. Multiply 152 by 63 using logarithms.

Solution.

log 152 = 2.1818

log 63 = + 1.7993

Sum

3.9811

antilog 3.9811 = 9.57 X 103

Thus, 152 x 63 = 9.6 X 103, with 2 significant figures

MD0837

1-37