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LOGARITHMS. 77
and to the mantissa of this logarithm corresponds the number
7 or 70 or 700 or 7000, etc., in the table of logarithms, but the
index of this logarithm is a cipher ; therefore the answer must
be a number consisting of one figure, thus it must be 7.
To Subtract a Larger Logarithm From a Smaller One.
This is the same as to divide a smaller number by a larger
one. Before the subtraction is commenced add 10 to the index
of the smaller logarithm (that is, to the minuend) and place
— 10 after the mantissa, then proceed with the subtraction as
if they were decimal fractions.
Example.
Divide 242 by 367 by means of -logarithms.
Solution:
Log. 242 = 2.383815 = 12.383815 — 10
Log. 367 = 2.564666
9.819149 — 10
and to the mantissa of this logarithm corresponds, according
to the table, the number 6594, but the negative index, 9 — 10,
indicates it to be 0.6594.
Thus, 242 divided by 367 = 0.6594.
Multiplication of Logarithms.
(involution.)
To multiply a logarithm is the same as to raise its corre-
sponding number into the power of the multiplier.
Logarithms having a positive index are multiplied the same
as decimal fractions. Thus
:
Square 224 by means of logarithms.
Solution:
2 X log. 224 = 2 X 2.350248 = 4.700496 = 50176
Logarithms having a negative index are multiplied the
same as decimal fractions, but an equal number is subtracted
from both the positive and the negative parts of the logarithm,
in order to bring the negative part of the index to — 10.
Example 1.
Square 0.82 by means of logarithms.
Solution
:
2 X log. 0.82 = 2 X (9.913814 — 10) = 19.827628 — 10, and
subtracting 10 from both the positive and the negative parts of
the logarithm, the result is 9.827628 — 10 ; this gives the num-
ber 0.6724.
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