 | Charles Davies - Geometry - 1870 - 392 pages
...equation (1) by equation (2), member by member, we have n »-. M ,.-*•, 10 = — or, m — « = log -=.: hence, The logarithm of the quotient of two numbers, is equal to tkt logarithm of the dividend diminished liy the logarithm of the divisor. Of Logarithme. 4. Siüce... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...we have mn = a**" ; therefore, log. mn = x-\-z = log. m-)-log. n. 4. — The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm bf the divisor. For, let m = a*, n = a* ; then x = log. w», z = log. n. By division we have _ = a*-*... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...by the other, member by member, we have ax+'=mn, in which x+y is the logarithm of the product mn. 4. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. For, dividing the equation a? = m by the equation a" = n, member by member, we... | |
 | Henry William Jeans - 1873 - 292 pages
...the 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 х=a-т-b, or -, then log. a;=log. a— log. b * For the proof of this general rule see... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. (" (1) 6-= yn; then, by def., log TO = x. Let ] ( (2) 6 l = n;... | |
 | 1873 - 192 pages
...(to six significant figures): (0x26534)^ V/(0.0357635) III. 1. Prove that the logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 2. Find, by logarithms, the values of the following quan*-• 3. Prove the formula (sin Af -f- (cos... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...75831.667. 5. Find the product of 85, .097, and .125. Ans. 1.03062. DIVISION BY LOGARITHMS. 16. Proposition. The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Г (1) b" = m; then, by def., log m = x. Let i. (_ (2) b * —... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...those numbers. Also, since powers of the same quantity are divided by subtracting their exponents, the logarithm of the quotient of two numbers is equal to the logarithm of the dividend diminished by that of the divisor. Since the logarithm of 10 is 1, if a number be multiplied or divided.by 10, its... | |
 | James Hamblin Smith - Trigonometry - 1877 - 244 pages
...of logarithms to the particular base 10, we may omit the suffix. 148. Tlie logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m=a*, and n=as. Then - = a-», •'• s. - = xy = Ioga m- log. »i. Thus tho operation of Division... | |
 | William Guy Peck - Calculus - 1877 - 238 pages
...function of x, S and we have, after reduction, fs + ds\ ,,/iZs ds* ds3 . But the logarithm of a quotient, is equal to the logarithm of the dividend, diminished by the logarithm of the divisor; changing the form of the first member and suppressing all the terms in the second member, after the... | |
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The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor. 
