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So LOGARITHMS.
Example.
* log. 2401 3.380392
Log. -v/2401 = —^ = 1 = 0.845098
and this logarithm corresponds to the number 7.
EXPONENTS.
The logarithm of a power divided by the logarithm of the
.root is equal to the exponent of the power.
Example.
8* = 64
log. 64
x =
x =
log. 8
1.80618
0.90309
2
The logarithm of a quantity under the radical sign divided
by the logarithm of the root is equal to the index of the root.
Example. x
8 = V512
x _ log. 512
log. 8
x _ 2.70927
0.90309
x =3
The reason for these last rules may be understood by re-
ferring to the rules for Involution and Evolution ; for instance
:
862 = 7396, and this expressed by logarithms is:
2 X log. 86 = log. 7396.
Therefore: ^ *396
= 2.
log. 86
FRACTIONS.
The logarithm of a common fraction is found, either by first
reducing the fraction to a decimal fraction, or by taking the
logarithm of the numerator and the logarithm of the denominator
and subtracting the logarithm of the denominator from the log-
arithm of the numerator ; the difference is the logarithm of
the fraction.
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