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.
Rewrite 3.4983 as 0.4983 - 3. This puts the logarithm in the form of an exponential
Antilog 0.4983 X antilog (-3)
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
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
Example. Multiply 152 by 63 using logarithms.
log 152 = 2.1818
log 63 = + 1.7993
antilog 3.9811 = 9.57 X 103
Thus, 152 x 63 = 9.6 X 103, with 2 significant figures