Logarithm*
15
SOLUTION:
1. Write the number as 2.03 x I0
2 .
2. In the log table, find 2.0 (sometimes written as 20) in the lefthand column.
Read across to the column under 3. This gives log 2.03 = 0.3075.
3. Because the exponent of 10 is 2, the characteristic is 2.
4. Log 203 = log 2.03 + log 10
2 = 0.3075 + 2 = 2.3075.
PROBLEM:
Find the log of 0.000203.
SOLUTION:
1. Write the number as 2.03 x IQ-".
2. As in the previous problem, find log 2.03 = 0.3075 (from the log table).
3. Because the exponent of 10 is -4, the characteristic is -4.
4. Log 0.000203 = log 2.03 + log lO'
4 = 0.3075 - 4 = -3.6925.
Interpolation
The log tables of this book show only three digits for N. If you want the log of a
four-digit number, you must estimate the mantissa from the two closest values
in the table. This process is called interpolation. For example, to find the log of
2032, you would proceed as follows.
Log 2032 = log (2.032 x 10J)
r
Mantissa of 2.04 = 0.3096
Mantissa of 2.03 = 0.3075
Difference between mantissas = 0.0021
The mantissa of 2.032 will be about 0.2 of the way between the mantissas of
2.03 and 2.04; therefore,
Mantissa of 2.032 = 0.3075 + (0.2 x 0.0021) = 0.3075 + 0.0004 = 0.3079
Log 2032 = log 2.032 + log 10
3 = 3.3079
Most hand calculators will provide logs for nine-digit numbers (a number
between 1 and 10 to eight decimal places), giving them to eight decimal places.
It would require a huge book of log tables to give (with much effort) the equiva-