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LOGARITHMS. 73
Log. 0.5 = 9.698970 — 10,
and Log. 500 = 2.698970, etc.
Thus, the mantissa of a logarithm is the same whether the
number is 0.5, 5, 50, 500, 5,000, etc. It is only the index that
is changed ; therefore, when a number consists of three or less
figures, its logarithm is found in the tables by taking the
mantissa found in the first column to the right of the number ;
that is, in the column under cipher. The index is found by the
same rule as before. For instance, logarithm to 537 will be
2.729974.
To Find the Logarithm of a Number Consisting of
Four Figures.
First find the figures in the column headed " N " corre-
sponding to the first three figures of the number ; in line with
these figures, in the column headed by the fourth figure, will be
found the mantissa of the logarithm corresponding to the
complete number. By prefixing the index, according to the
rule already given, the complete logarithm is obtained.
Example.
Find logarithm of 5375.
Solution
:
Under the heading " N " find 537 ; and in the column at the
top of the table find "5"; under 5 in the line with 537 is
730378.
This is the mantissa of the logarithm. The index for a
number consisting of four integers is 3, therefore the complete
logarithm of 5375 is 3.730378.
To Find the Logarithm of a Number Having Hore Than
Four Figures.
Example 1.
Find the logarithm to 3658.2.
Solution
:
Log. 3658 — 3.563244 and log. 3659 = 3.563362 ; therefore the
logarithm for 3658.2 must be somewhere between the two logar-
ithms thus found in the table. The difference between these
two logarithms is 0.000118; that is, if- the number is increased
by 1 the logarithm increases 0.000118, therefore if this number
is increased 0.2 the corresponding logarithm must increase 0.2
times, 0.000118 = 0.0000236, which may be taken as 0.000024.
Thus
:
Log. 3658 = 3.563244
Difference corresponding to 0.2 = 0.000024
Log. 3658.2 = 3.56326S
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