| Webster Wells - 1885 - 368 pages
...4771, log 5 = .6990, log? = .8451 ; find the values of the following : 344. The logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume the equations 10*=ml; whence, }* = logm. 10» = n ) (-У — logn. »•*i» £-™,•"0'—™•... | |
| Webster Wells - Plane trigonometry - 1887 - 150 pages
....6990, log? = .8451 ; find the values of the following : 92. In any system, the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume the equations ax = m] (x = \ogam, }• ; whence, < . , • 2. log6. 7. log 21. 12. log 98. 17.... | |
| Webster Wells - Trigonometry - 1887 - 196 pages
....6990, log 7 = .8451 ; find the values of the following : 92. In any system, the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume the equations ' x = loga m, : log„ n. a" = m ) , ( x = ] > ; whence, .j 2. loge. 7. log 21.... | |
| Edward Albert Bowser - Algebra - 1888 - 876 pages
...of factors. Thus, log 30 = log (2 x 3 X 5) = log 2 + log 3 + log 5. (5) The logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** For let — be the fraction, and suppose n x = logm, y — log n. Then m = a*, n = a". Vfi fl*^ Therefore... | |
| Webster Wells - Algebra - 1889 - 584 pages
...5. log 84. 10. log 144. 15. log 375. 20. log 14406. 408. In any system, the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume the equations [• ; whence, •! - a" ' cf = n ¡ (.y = lOga'1т^. . ,. . a* mm Dividing, we... | |
| Webster Wells - Algebra - 1890 - 560 pages
...log6048. 4. Iog63. 8. log210. 12. log 686. 16. logl2005. 500. In any system, the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume the equations °'r=™J; whence, Dividing, we have — = ™, or aj~r = m. a* nn Whence, log.—... | |
| John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...way the theorem can be extended to any number of factors. 106. Theorem 2. The logarithm of a quotient **is equal to the logarithm of the numerator minus the logarithm of the denominator.** щ Let — be the quotient, a the base ; we have to show that n log. - = log. m - log. и. n .Let m... | |
| Henry Sinclair Hall, Samuel Ratcliffe Knight - Algebra - 1895 - 508 pages
...of a product is equal to the sum of the logarithms of its factors. (2) The logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** (3) The logarithm of any power, integral or fractional, of any quantity is equal to the logarithm of... | |
| George Washington Hull - Algebra - 1895 - 358 pages
...= log 2 + log 3. log 2 = 0.3010 Iog3 = 0.4771 log 6 = 0.7781, Ans. « EXAMPLES. 275. The logarithm **of the quotient of two numbers is equal to the logarithm, of the** dividend minus the logarithm of the divisor. Let m and n be any two numbers, and x and ,i/ their logarithms.... | |
| William Freeland - Algebra - 1895 - 328 pages
...factors. 394. IV. Also if m* = a, and m? = b, m*-" = -. Hence, b log - = x — y ; that is, the logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the divisor. 395. V. Again, if. m* = a, m1" = af, and log ar = px =... | |
| |