LOG
LOG
Right again, and it makes 4456320, which isthe Number nearly corresponding to the Loga-rithm 6.648976^
Addition, Subjlr action. Multifile at tonand Division in Logarithms.
3. In the Addition of two or more Logarithmstogether, observe these Rules.
1. If all the Indices be Integers, add them asis usual in common Arithmetics.
1. If the Indices be some Integers, and somethe Indices of Parts, or Fractions, they will bounlike ; and therefore if when added their Sumbe 1 o, or above, cast away x o, the Remainder
is the Index of Integers; if under 1 o, Decimal
Parts. Thus, 8
2. 057821' i. 237242
7.583210 9.875062
-• 8.698971
9.641031 - - -
-.... >. 0.811275
3. If the Indices be all Decimals, and whenadded make a Sum under 1 o, then add 1 o tothe Sum ; if just 1 o, then add Unity; if above1 o, cast x o away, and the Index thus gotten isalways Decimal Parts. Thus,
9^39794* 8.698972
9.875062 9.875061
9. 273003 8. 574033
4. Subfir action of Logarithms.
1. If the Indices be Integers, then proceed asusually.
2. If the Indices be either of them, or bothDecimal Parts, observe whether the Index ofthe upper Quantity be a smaller Number thanthat of the Subtrahend or the lower j is it be,add 1 o to it; and if the upper be of a greaterValue than the lower, (that is, a bigger Indexby Place) then the Remainder will be Integers 5if nor, Decimal Parts.
Examples.
2.033421 9.875062 9.87506a 1.235781
^875062 2.033421 8.574031 3.572141
2.158359 7.841641 1.301031 7.663640
J. T he Logarithm of a Fraction is thus found.
Substract the Logarithm of the Denominatorfrom the Logarithm of the Numerator; the Re-mainder gives the Logarithm of the Fraction,as of {- j the Logarithm of 4 is 0.602060, outof the Logarithm of 3, 0.477121, the Difference9. 875061 is the Logarithm of i or 75.
6. To Multiply a Logarithm.
If the Index be negative, observe that in mul-tiplying the Figure next the Index, the Tens to
be carried in Mind are affirmative, and a#be deducted out of the Product of thcflcg* 0Indices. Thus,
2. 5432113
5.629633
1. 9872145
93607c
isi
7. To Divide a Logarithm, having * b
or Fractional Index. jj.
Observe whether the Divisor willvide the Index, then there is no iV
if it do not evenly divide the Index, ad jy di'Index so many Unites, till it may be ^ j„.
vided, setting the Quotient down f° r A- $$dex, augmenting the next Figure by 10times 1 o as you added to the first.
2) 5- 6llli
2 Zo6l4
8. Multiplication of Numbers by the
3) 5-3214-22.440470
;lG
Add the Logarithms of the pr^
ther, and the Sum is the Logarithmduct required.
Multiplicand 32Multiplier 5 2
1.50515°
1.716003
221153
9. Division of Numbers by Log 31 '* 11
This is done only by substracti n ?[j), of ^rithm of the Divisor from the Logo's r be VDividend; and the Remainder wil*
garithm of the Quotient.
Dividend 7286 3.862489 .55 1 *
Divisor
505150
2-357359
Quotient 227.8
1 o. Extraction of Square, Cube) ^by Logarithms.
To extract the Square Root of WJ’
is to divide the Logarithm of that N u •for the Cube Root by 3, &c. That ^ thedivide the Logarithm of the Numberdex of the Power.
Number 75832Sq. Root 275.37
Cube Root 42.327
Log. 4.87985* for ^2) 2.4399^2^^
■ivt*
the
z) X. 626614^
it. To find a mean Proportional bet
Numbers, by Logarithms- ^
Half the Sum of their Logarithm* 8Logarithm of the mean Proporti° nthem.
The Numbers are ^ ^ °.z°t 110
Mean Proportional
12 . r