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7 2
Log.
LOGARITHMS.
1=0 because 10° = 1.
10 = 1 101 = 10.
100 = 2 102 = 100.
1,000 = 3 103= 1,000.
0,000 = 4 104 = 10,000.
The logarithm of any number between 1 and 10 is a frac-
tion smaller than 1. The logarithm of any number between 10
and 100 is a number between 1 and 2. The logarithm of any
number between 100 and 1000 is a number between 2 and 3, etc.
The decimal part of the logarithms is called .the mantissa^
and is given in the table commencing on page 88.
The integer part of a logarithm is called the index or some-
times the characteristic, and is not given in the table, but
is obtained by the rule that it is one less than the number
of figures in the integer part of the number ; thus, the index of a
logarithm for any number consisting of two figures must be 1;
the index of the logarithm for a number consisting of three
figures must be 2, etc.
The index of the logarithm of a decimal fraction is a nega-
tive number. Sometimes the negative index is denoted by
writing a minus sign over it; for instance, log. 0.5240 = 1.719331,
or the negative index is denoted by writing it after the mantissa ;
thus, log. 0.5240 = 9.719331 — 10. This, of course, is of exactly
the same value whether written — 1 or 9 — 10. Either of
these expressions is jninus one in value, but it is more con-
venient in logarithmic calculations to write the negative index
after the mantissa ; thus, instead of writing 1, write 9
— 10 ; instead of 2, write 8 — 10, etc. Only the mantissa
is given in the table, but the index (as already explained) is
obtained by the rule: One less than the number offigures on
the left side of the decimal point . Therefore, in order to
memorize and explain this rule, the following examples are
inserted
:
Number. Logarithm. Number. Logarithm.
8236
823.6
82.36
8.236
0.82-36
3.915716
2.915716
1.915716
0.915716
9.915716 — 10
0.08236
0.008236
0.0008236
0.00008236
0.000008236
8.915716—10
7.915716 — 10
6.915716 — 10
5.915716 — 10
4.915716 — 10
Multiplying or dividing a number by any power of 10
does not change the mantissa in the corresponding logarithm,
but only the index ; for instance :
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