« ΠροηγούμενηΣυνέχεια »
Here the 2, to be carried, cancels the 2, and there re. mains the I to be set down.
DIVISION BY LOGARITHMS.
From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
NOTE. If i be to be carried to the index of the subtrahend, apply it according to the sign of the index; then change the sign of the index to -, if it be t, or to ti if it be ; and proceed according to the second note una der the last rule.
1. To divide 24163 by 45677
ܕ!,x ܀ ܕ
2. To divide 37*149* by 523*76.
3. Divide .06314 by ‘007245.
Quotient 8.719792 o'9405061 Here 1, carried from the decimals to the 3, makes it become-2, which, taken from the other 2, leaves o remaining. 4. To divide •7438 by 12'9476. Num.
Here the 1, taken from the 1, makes it become to be set down.
INYOLUTION BY LOGARITHMS.
Multiply the logarithm of the given number by the index of the power, and the number answering to the product will be the power required.
Note. A negative index, multiplied by an' affirmative number, gives a negative product ; and as the number carried from the decimal part is affirmative, their difference with the sign of the greater is, in that case, the index of the product
1. To square the number 2'5791.
2. To find the cube of 3*07146.
To raise *09163 to the 4th power.
Here 4 times the negative index being -8, and 3 to be carried, the difference - 5 is the index of the product.
97495 116994 58497
EVOLUTION BY LOGARITHMS.
Divide the logarithm of the given number by the index of the power, and the number answering to the quotient will be the root required.
Note. When the index of the logarithm is negative, and cannot be divided by the divisor without a remainder, increase the index by a number, that will render it exactly divisible, and carry the units borrowed, as so many tens, to the first decimal place; and divide the rest as usuala
1. To find the square root of 365.
2. To find the 3d root of 12345.
3. To find the roth root of 2,
4. To find the 365th root of 1'045.
5. To find the second root of '093. Num.
2)-2.9684829 Root '304959
Here the divisor 2 is contained exactly once in the negative index -2, and therefore the index of the quotient is
6. To find the third root of '00048.
Here the divisor 3 not being exactly contained in 4, 4 is augmented by 2, to make up 6, in which the divisor is contained just 2 times; then the 2, thus borrowed, being carried to the decimal figure 6, makes 26, which, divided by 3, gives 8, &c.