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LOGARITHMS.
Solution
log. 0.125 _ 9.09691—10 _ 29.09691—80 _ Q
QQ8Qrj _ 1Q
3 3 3
and to this logarithm corresponds the number 0.5.
Example 3.
Extract the 1.7 root of 0.78.
Solution
:
log. 0.78 9.892095 — 10
L7
~"
L7
We cannot here, as in previous examples, add a multiple of
10 to the index on each side of the mantissa, but 7 must be
added in order that the negative quotient shall be — 10 after
the division is performed. Thus
:
9.892095 — 10 16.892095 — 17 n IW.,,, -m
— = 9.9obo2b — 10
1.7 1.7
and to this logarithm corresponds the number 0.864.
Short Rules for Figuring by Logarithms.
MULTIPLICATION.
Add the logarithms of the factors and the sum is the logar-
ithm of the product.
DIVISION.
Subtract divisor’s logarithm from the logarithm of the divi-
dend and the difference is the logarithm of the quotient.
INVOLUTION.
Multiply the logarithm of the root by the exponent of the
power and the product is the logarithm of the power.
Example.
Log. 862 = 2 X log. 86 = 2 X 1.934498 = 3.868996
and to this logarithm corresponds the number 7396.
EVOLUTION.
The logarithm of the number or quantity under the radical
sign is divided by the index of the root and the quotient is the
logarithm of the root.
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