Use of Logarithms in Division

NOTE:

If you were to multiply these two numbers together by the usual method you

would have obtained 9576 instead of 9570 as was determined by the use of

logarithms due to the accuracy of the logarithm tables. Logarithms are

approximate values.

1-40. USE OF LOGARITHMS IN DIVISION

To divide two numbers, the logarithms of the numbers are subtracted; i.e., the

logarithm of the divisor (denominator) is subtracted from the logarithm of the dividend

(numerator). The antilogarithm of the difference of logarithms is then taken to give the

quotient.

Example. Divide 152 by 63 using logarithms.

Solution.

log 152 = 2.1818

log 63 = -1.7993

Difference 0.3825

antilogarithm of 0.3825 = 2.41

Thus, 152 divided by 63 = 2.4, with 2 significant figures

1-41. USE OF LOGARITHMS TO FIND ROOTS OF NUMBERS

To find the root of a number, the logarithm of the number is determined; the

logarithm of the number is next divided by the root desired; e.g., if the square root of a

number is wanted, the logarithm of the number is divided by two; if the cube root is

required, divide by three, etc. The antilogarithm of the quotient is taken; the resulting

number is the root of the number.

a. Example 1. Find the square root of 625.

Solution.

Square root 625 = (625)1/2

log (625)1/2 = 1/2 log 625 = 1/2 X 2.7959 = 1.3980

antilogarithm 1.3980 = 25.0

Thus, the square root of 625 = 25.0

MD0837

1-38