| Charles Davies - Geometry - 1870 - 319 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 - 420 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
...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 - 164 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 - 276 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 - Geometry - 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 - 228 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 - 208 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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