| Webster Wells - Trigonometry - 1896 - 236 pages
...12005. 5. log 75. 9. log 210. 13. log 686. 17. log 15876. 77. 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 a = m. whence f > "*1вИВв, .i a* = n > (i/ = logan. Dividing the assumed equations,... | |
| Webster Wells - 1897 - 422 pages
...6. log 40. 11. log 625. 16. log 686. 21. log 15876. 398. 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 a' = m\ <x = legam, \ ; whence, \ a? — nl ( ;j = log. н. Dividing the assumed... | |
| Webster Wells - Algebra - 1897 - 378 pages
...3 = .4771, log 5 = .6990, and log 7 = .8451, find: 398. In any system, the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** 2. log 35. 7. log 126. 12. log 324. 17. log 1125. 3. log 50. 8. log 196. 13. log 378. 18. log 2625.... | |
| Andrew Wheeler Phillips, Wendell Melville Strong - Trigonometry - 1898 - 376 pages
...is equal to the sum of the logarithms of the numbers. Thus loga;//я = logaw + logeя. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the divisor. Thus log»— — logam — logan. n The logarithm of... | |
| Daniel Alexander Murray - Plane trigonometry - 1899 - 342 pages
...product of any number of factors is equal to the sum of the logarithms of the factors. (2) T7(e logarithm **of the quotient of two numbers is equal to the logarithm of the numerator** diminished by the logarithm of the denominator. (4) The logarithm of the rth root of a number is equal... | |
| Pitt Durfee - Plane trigonometry - 1900 - 340 pages
...above by the second, m 10* m — = — = 10x-v, or log— = x — y = log m — logn. II. The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the . divisor. Kaising m = 10J; to the /,'th power, ink = 10*'*, or... | |
| James Harrington Boyd - Algebra - 1901 - 818 pages
...+ logap. [(6)] E. g. Loge 42= loge (2x3x7) = loga2+loga3 + loga7. 6. The logarithm of aj 'ˇ-action **is equal to the, logarithm of the numerator minus the logarithm of the denominator.** Thus m — loga Proof. — Let — be the fraction, and suppose (1) m = a*, and (2) n = о». By ?55б... | |
| James Harrington Boyd - Algebra - 1901 - 816 pages
...loga/>. [(6)] E. g. Log0 42 = Iog0 (2x3x7) = loge2+loga3 + log07. 6. The logarithm of a fraction it **equal to the logarithm of the numerator minus the logarithm of the denominator.** Thus bga ^ = loga m — logan. Proof. — Let •- be the fraction, and suppose (1) m = a-, and (2)... | |
| William James Milne - Algebra - 1901 - 460 pages
...common base represent exponents of the same number, it follows that : 466. PRINCIPLE. — The logarithm **of the quotient of two numbers is equal to the logarithm of the** dividend minus the logarithm of the divisor; that is, To any base, log (m ч- n) = log m — log n.... | |
| American School (Chicago, Ill.) - Engineering - 1903 - 392 pages
...for a; and y their values, loga mn = loga m -f- loga n 62. In any system the logarithm of a fraction **is equal to the logarithm of the numerator minus the logarithm of the denominator.** Assume ax = m (1) J Then ( loga m = x And a" = n (2) j by § 56 j loga n = y Divide equation (1) by... | |
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