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" ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. "
Elements of Geometry and Trigonometry - Page 232
by Adrien Marie Legendre - 1838 - 269 pages
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Essentials of Algebra for Secondary Schools

Webster Wells - Algebra - 1897 - 384 pages
....3010, log 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....
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College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...+ logap. [(6)] E. g. Loge 42= loge (2x3x7) = loga2+loga3 + loga7. 6. The logarithm of aj '¡-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...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 812 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)...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903 - 392 pages
...Substituting 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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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 484 pages
...log 2646. 3. log 84. 6. log 392. 9. log 1372. 12. log 24696. 422. 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' = nj' I; Dividing the assumed equations, а- = ™,ora~' = ??....
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Algebra for Secondary Schools

Webster Wells - Algebra - 1906 - 550 pages
...log 2646. 3. log 84. 6. log 392. 9. log 1372. 12. log 24696. 422. 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 = t ; whence, \ o» = » Г \y = x = log.m, log.«. Dividing the assumed...
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A First Course in Algebra ; A Second Course in Algebra

Webster Wells - Algebra - 1908 - 456 pages
...log 2646. 3. log 84. 6. log 392. 9. log 1372. 12. log 24696. 88. 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 } v. Í x = log* m> ; whence, a" = n } [y = iogan. Dividing the assumed...
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Plane Trigonometry

Edward Rutledge Robbins - Logarithms - 1909 - 184 pages
...г/ (Def. of log). . •. log M • N = log M + log N (substitution). 89. THEOREM. The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Given: The fraction — • To Prove: log — = log .if— log N. NN Proof : Suppose 10* = M] flog...
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How to Use a Table of Logarithms

Edward Vermilye Huntington - Logarithms - 1912 - 32 pages
...logarithm of the first factor plus the logarithm of the second factor; (2) The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator; (3) The logarithm of the nth power of a number is equal to n times the logarithm of the number; (4)...
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Plane Trigonometry and Applications

Ernest Julius Wilczynski - Plane trigonometry - 1914 - 296 pages
...of the divisor. The same fact may, of course, be stated in the equivalent form: the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. According to the third index law (Art. 17, equation (3)), we have '° Therefore, we find from (1) M"...
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