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LOGARITHMS. 75
number is to have three figures on the left-hand side of the
decimal point ; thus, the number corresponding to the logarithm
2.610979 will be 408.3. ,
Example 2.
Find the number corresponding to the logarithm 3.883991.
Solution
:
This mantissa is not in the table. The nearest smaller
mantissa is 883945, and to this mantissa corresponds the number
7055. The nearest larger mantissa is 884002, and to this
corresponds the number 7656.
Thus, an increment in the mantissa of 57 increases the
number by 1, but the difference between the mantissa 883945
and S83991 is 46, therefore the number must increase ff = 0.807.
Number of Log. 3.883945 = 7655
Difference 0.000046 = 0.807
Number of Log. 3.883991 = 7655.807
Addition of Logarithms.
(MULTIPLICATION.)
Where the logarithms of the factors have positive indexes,
add as if they were decimal fractions, and the sum is the log-
arithm corresponding to the product.
Example
Multiply 81 by 65 by means of logarithms.
Solution
:
Log. 81 = 1.908485
Log. 65 = 1.812913
3.721398
and to this mantissa corresponds the number 5265. The index
is 3; therefore the number has no decimals, as it consists of only
four figures.
To Add Two Logarithms when One Has a Positive and
the Other a Negative Index.
Example
Multiply 0.58 by 32.6 by means of logarithms.
Solution
:
Log. 0.58 = 9.763428 — 10
Log. 32.6 = 1.513218
11.276646 — 10
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