Plane trigonometry, by S.L. Loney.

CHARACTERISTIC OF ANY LOGARITHM.

151

The logarithm of any number between 1 and '1 therefore lies between 0 and -1, and so is equal to - 1 + some
decimal, i.e. its characteristic is 1.
So the logarithm of any number between '1 and '01
lies between 1- 1 and -2, and hence it is equal to - 2 +
some decimal, i.e. its characteristic is 2.
Similarly the logarithm of any number between '01
and '001 lies between - 2 and - 3, i.e. its characteristic is 3.
Generally, the characteristic of the logarithm of any
decimal fraction will be negative and numerically will be
greater by unity than the number of cyphers following the
decimal point.
For any fraction between 1 and '1 (e.g. '5) has no
cypher following the decimal point and we have seen that
its characteristic is 1.
Any fraction between '1 and '01 (e.g. '07) has 1 cypher
following the decimal point and we have seen that its
characteristic is 2.
Any fraction between '01 and '001 (e.g. '003) has two
cyphers following the decimal point and we have seen that
its characteristic is 3.
Similarly for any fraction.
Exs. The characteristic of the logarithm of the number -00835 is 3.
The characteristic of the logarithm of the number '0000053 is 6.
The characteristic of the logarithm of the number '34567 is 1.
143. The mantissce of the logarithm of all numbers,
consisting of the same digits, are the same.
This will be made clear by an example.
Suppose we are given that
log 66818 = 4-8248935.