Number of digits to the
left of the decimal
c. Example 1. Find the antilogarithm of 2.000.
Solution. Determine the digits that correspond to the mantissa. The mantissa
is .000 and the digits corresponding to this mantissa in the table of "common"
logarithms are 100. The characteristic of two indicates that there are three digits or
places to the left of the decimal point. Thus, antilog 2.000 = 100. To check your
answer, take the logarithm of 100:
log 100 = 2
d. Example 2. Find the antilogarithm of 3.2989.
Solution. The digits corresponding to the mantissa (0.2989) are 199. The
characteristic indicates that there are four digits to the left of the decimal point.
Therefore, antilog 3.2989 = 1990.
e. Example 3. Find the antilogarithm of 3.2989.
Solution. Rewrite 3.2989 as 0.2989 - 3. This puts the logarithm in the form of
an exponential expression. Take the antilogarithm of both numbers.
Antilog 0.2989 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 antilogarithm of 0.2989 = 1.99
The antilogarithm of minus three (-3) is 10-3
Thus, the antilogarithm of 3.2989 = 1.99 x 10-3
f. Example 4. Use the logarithm table to find the antilogarithm of -2.5017, a
logarithm from an electronic calculator.