 | Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...multiplication we have mn = a*+* ; therefore, log. mn = x-\-z = log. m-|-log. и. 4. — The logarithm of q quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For, let m = a", n •=. a* ; then x = log. m, z = log. n. By division we have _ — a»-» • я... | |
 | Isaac Todhunter - Plane trigonometry - 1866 - 216 pages
...log. n ; therefore m = a*, and n — a'; therefore nin = therefore log. mn = 54. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. For let x=\og,m, and y=\og,n; therefore m=a", andn=o»; therefore ™ = *=a"-'; n a° therefore log.... | |
 | James Hamblin Smith - 1869 - 412 pages
...m = a', and n = a". Then mn = a'+s ; «'. log ти = x + y = log m + log n. 372. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. Let m = a', and и = a?, Then - = a"i; n m log m - log n, 373. The logarithm of any power of a number... | |
 | James Hamblin Smith - Algebra - 1870 - 478 pages
...are treating of logarithms to the particular base 10, we may omit the suffix. 456. The 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 - = o"-'; n =logant- logan. Thus the operation of Division is changed into... | |
 | Isaac Todhunter - Algebra - 1870 - 626 pages
...a"; therefore mn = a1 a" = et**; therefore loganm = x + y = logam + logaw. 536. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor. thereforo m = a", n = a? ; ma!° therefore — = — = a"-" ; no? therefore Iog0 - =x — y = logam... | |
 | James Hamblin Smith - Algebra - 1870 - 452 pages
...are treating of logarithms to the particular base 10, we may omit the suffix. 456. The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the dicisor. Let m=a*, and n = a". Then ™ = a"-»; •• a = log(Jm-logan. Thus the operation of Division... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...multiplication 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*-*... | |
 | 1873 - 192 pages
...quantities (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... | |
 | Henry William Jeans - 1873 - 292 pages
...: 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... | |
 | Benjamin Peirce - 1875 - 306 pages
...number divided by the exponent of the root. 13. Corollary. The equation log. m m' = log. m + log. m' t gives log. m' = log. m m' — log. m; that is, the...dividend, diminished by the logarithm of the divisor. 14. Corollary. We have, by arts. 13 and 9, log - ~n = } ° S - l ~ log - n = — log. n ; Logarithms... | |
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The logarithm of the quotient is equal to the logarithm of the dividend, diminished by the logarithm of the divisor. 
