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
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
Example. Divide 152 by 63 using logarithms.
log 152 = 2.1818
log 63 = -1.7993
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.
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