2.30 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSAlgebra
Hence, log 23 = 1.3617.
Let us now find the logarithm of 234, its characteristic evidently is 2, if we move across horizontally starting
from 23 and stop just below 4 of the central column, we find the figure 3692.
Hence log 234 = 2.3692.
Lastly, to find the logarithm of 2345, we see the characteristic is 3. Now starting form 23, if we stop below 4
of the central column we get the figure 3692. Again if we move further across the same horizontal line and
stop just below 5 in extreme right column of mean difference, we get figure 9. Now adding these two
figures, we find 3701, i.e., (3692 + 9).
Hence log 2345 = 3.3701
Similarly we have,
log 1963 = 3.2929
log 43.17 = 1.6352
log 7.149 = 0.8542.
For number of 5 digits
Suppose we are to find the value of log 23.456. Form 4 figure logarithmic table we get.
log 23.4 = 1.3692
Difference for (4th digit) 5 = 9
Difference for (5th digit) 6 = 1 1= 1.3702
Rule for carry over number from the difference table :
For 0 to 4, carry over 0
5 to 14, carry over 1
15 to 24, carry over 2 and so on.
USE OF ANTILOGARITHMIC TABLE :
The antilog, gives us numbers corresponding to given numbers. At first we are to find the number
corresponding to given mantissa and then to fix up the position of the decimal point according to the
characteristic.
For example, to find antilog 1.5426. Now from the antilog table we can see, as before, the number
corresponding to the mantissa.
0.5426 is 3483 + 5 = 3488. Since the given characteristic is 1, the required number is 34.88.
Hence log 34.88 = 1.5426, since antilog 1.5426 = 34.88.
Example 39 : If log 3 = 0.4771, find the number of digits in 3^43.
solution:
Let x = 3^43 then log x = log 3^43 = 43 log 3.
or log x = 43 × 0.4771 = 20.5153. Here the characteristic in log x is 20. So the number of digits in x will be 20 +
1 = 21.