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The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor.
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... - Page 262
by Benjamin Peirce - 1837 - 288 pages

## A Treatise on Algebra

George Peacock - Algebra - 1830 - 732 pages
...Log' — ; = log' n — log' n', or the logarithm of the n quotient of two numbers or quantities, is the logarithm of the dividend diminished by the logarithm of the divisor, and conversely. (3) Log' np=p log' n, or the logarithm of the pA, or any power of a number is found...

## An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1837 - 288 pages
...the logarithm of any root of a number is equal to the logarithm of the number divided by the exponent of the root. 11. Corollary. The equation log. m m'...have, by arts. 11 and 7, log. - = log. 1 — log. n IV =. — log. n ; that is, the logarithm of the reciprocal of a number is the negative of the logarithm...

## A Treatise on Algebra: Embracing, Besides the Elementary Principles, All the ...

George Roberts Perkins - Algebra - 1842 - 360 pages
...respective logarithms ; and (Art. 218) the logarithm of the quotient of one quantity divided by another is equal to the logarithm of the dividend diminished by the logarithm of the divisor, we find for the logarithm of our expression 3.75X1.06 log. - - =log. 3.75+log. 1.06-log. 365. By the...

## Plane and Spherical Trigonometry ...

Henry W. Jeans - Trigonometry - 1842 - 138 pages
...product : thus if x=ab then log. A =log. a + log. b. (b) The logarithm of the quotient of any two numbers is equal to the logarithm of the dividend diminished by the logarithm of the divisor : thus if x = 7 then log. x = log. a — log. b. If x = — then log. x=log. a+log. b 00 + log. c —...

## An Elementary Treatise on Algebra: To which are Added Exponential Equations ...

Benjamin Peirce - Algebra - 1843 - 308 pages
...of the number divided by the ezponent of the root. 13. Corollary. The equation log. m mf = log. m 4- log. m', gives log. m' = log. m m' — log. m ; that...dividend, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log. — = log. 1 — log. n = — log. n ; Logarithms in...

## Elements of Surveying and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1852 - 412 pages
...member, we have, MM 10m n = i^or, m — n = logjr: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product of any number by 10, will be greater...

## Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...have, mn MM 10 -=_r~0r, ra — tt = log-r^: hence, The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product of any .number by 10, will , be greater...

## Elements of Surveying, and Navigation: With Descriptions of the Instruments ...

Charles Davies - Navigation - 1854 - 444 pages
...member, we have, 10m~n = -^or, m — n~logj^: hence, The logarithm of the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 5. Since the logarithm of 10 is 1, the logarithm of the product of any number by 10, will be greater...