 | James Morford Taylor - Algebra - 1900 - 504 pages
...N= ax+». § 346 Hence loge(3f y, N) = x + y = loga M -\- log. N. 442. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. Proof. Let M=a', N=a'; then M-*-N=a"'. §346 Hence log. (M •+• N) = ж — у = log, M — log,... | |
 | William James Milne - Algebra - 1901 - 476 pages
...numbers to a common base represent exponents of the same number, it follows that : 466. PRINCIPLE. — The logarithm of the quotient of two numbers is equal...of the dividend minus the logarithm of the divisor; that is, To any base, log (m ч- n) = log m — log n. The above principle may be established as follows:... | |
 | William James Milne - Algebra - 1901 - 462 pages
...exponents of the same number, it follows that: 466. PRINCIPLE. — The logarithm of the quotient oftivo numbers is equal to the logarithm of the dividend minus the logarithm of the divisor; that is, To any base, log (m -=- и) = log m — log n. The above principle may be established as follows:... | |
 | George Egbert Fisher - 1901 - 622 pages
...2048 = 32 • 64, we have Iog2 2048 = logj 32 + logj 64 = 5 + 6 = 11 7. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, loge (m -r- n) = Iog6 m — log,, n. Let logj m = x and logb n = y; then Ъх = m and b* = n, and... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 646 pages
...Since 2048 = 32-64, we have log, 2048 = log, 32 + log, 64 = 5 + 6 = 11. 16. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, log» (m -i- n) = logt 14 — logu "• Let log» m = x and log» я = jr ; then b* = m and 6»... | |
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...• ay = az+v. 4. .-. loga mn = x + y = loga m + loga n. 468. Prop. 4. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. 977 Dem. Let -- be the given quotient, m being the dividend 7Î- * » 1. For let x = log„rw and y... | |
 | Ernest Smith Awmack Robson - Heat - 1902 - 212 pages
...logarithm has a mantissa of .5150 ; .-. antilog of 1.5150 = 32.73 ; .'. 23. 12 X 1.416 = 32.73. (2) The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numerator and denominator or log a\b = log a - log b. Eg (i.) log... | |
 | James Morford Taylor - History - 1904 - 192 pages
...Hence loga(Jf x N) = x + y = IogaЛf+ logaJV. (ii) The logarithm of the quotient of two arithmetic numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Let Ж = a*, N=w1. Then M+N = a*-v. Hence loga(M- N) = x — y = logaM — \ogaN. (iii) The logarithm of... | |
 | James Morford Taylor - Trigonometry - 1905 - 256 pages
...Hence loga(Af x N) = x + y = logaJtf + logaN. (ii) The logarithm of the quotient of two arithmetic numbers is equal to the logarithm of the dividend minus the logarithm of the divisor. Let If = a«, N =a)i. Then Ж ч. N = a*- ». Hence loga (AT •*• N) = x — y = log«, Af - loga.2v".... | |
 | Walter Randall Marsh - Algebra - 1905 - 412 pages
...proved for the product of three or more factors. II. The logarithm of the quotient of two numbers is the logarithm of the dividend minus the logarithm of the divisor. Let 10" = ж, or log x = a, (1) and let 10* = y, or log у = b, (2) dividing (1) by (2), 10" - '' = -,... | |
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The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log 
