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7 6 LOGARITHMS.
This reduces to 1.276646 and to this logarithm corresponds
the number 18.908. This mantissa, 276646, cannot be found in the
table, but the nearest smaller mantissa is 276462, and the differ-
ence between this and the next is found by subtraction to be
230, and the difference between this and the given mantissa
is 184.
Thus:
Given logarithm 1.276646
To the tabulated log. 1.276462 corresponds 18.90
Difference 0.000184 gives 0.008
Thus, logarithm 1.276646 gives number 18.908
To Add Two Logarithms, Both Having a Negative
Index.
Add both logarithms in the same manner as decimal frac-
tions, and afterwards subtract 10 from the index on each side
of the mantissa.
Example.
Multiply 0.82 by 0.082 by means of logarithms.
Solution
:
Log. 0.82 = 9.913814 — 10
Log. 0.082 = 8.913814 — 10
18.827628 — 20
By subtracting 10 on each side of the mantissa this logar-
ithm reduces to 8.827628 — 10 and to the mantissa 82762S corre-
sponds the number 6724, but the negative index 8 ..... .
— 10
indicates that this first figure 6 is not a whole number, but that
it is six-hundredths ; therefore a cipher must be placed between
this 6 and the decimal point in order to give 6 the right value
according to the index; thus, to the logarithm 8.827628 — 10
corresponds the number 0.06724.
Subtraction of Logarithms.
(DIVISION.)
Logarithms are subtracted as common decimal fractions.
To Subtract Two Logarithms, Both Having a Positive
Index.
Example.
Divide 490 by 70 by means of logarithms.
Solution
:
Log. 490 = 2.690196
Log. 70 — 1.845098
0.845098
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