 | 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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N .-. by definition, x — x" is the logarithm of ^ ; that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation... 
