 | Elias Loomis - Algebra - 1846 - 380 pages
...16000 = log. 1600 = 4* + 2, log. 160000 —, &c. We have seen, in Art. 323, that the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Hence, log. (y) = log. 5 = 1 — x. Hence, log. 50 = '2 — x, log. 5000 = log. 500 =3 — x, log.... | |
 | Charles William Hackley - Algebra - 1847 - 503 pages
...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 (1) to the nth power. N"=a". .-. by definition, nx is the logarithm... | |
 | John Bonnycastle - 1848 - 334 pages
...PQKS = cf. af . a' . a" = a"+'+„ + „; hence log.PQBS = (2) The logarithm of a fractional quantity is equal to the logarithm of the numerator minus the logarithm of the denominator. Let a" = P and a* = Q, then x = }ogje and y = log.Q ; hence Q ~ u-- - ' .-. log,- — xy — log.P—... | |
 | Charles Davies - Trigonometry - 1849 - 384 pages
...was nearer 57 than 56; hence it would have been more exact to have added the former number. inator. The logarithm of a decimal fraction is found, by considering...logarithm a negative characteristic, greater by unity t/ian the number ofciphers between the decimal point and the first significant place of figures. Thus,... | |
 | John Bonnycastle - Algebra - 1851 - 288 pages
...Hence, the logarithm of a fraction, or of the quotient arising from dividing one number by another, is equal to the logarithm of the numerator minus the logarithm of the denominator. And if each member of the common equation a? — y be raised to the fractional power denoted by —... | |
 | Joseph Ray - Algebra - 1852 - 410 pages
...first member to a form in which it shall also be divisible by the same factor. Since the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator (Art. 361), therefore, log. (14*)- log. (14*)= log. ( j±j? ) . But, by division, we find ^J=l-\-~... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...log. 16000 = log. 1600=4a;+2, log. 160000=, &c. We have seen, in Art. 339, that the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Hence, log. 5= log. (y) = l— a;. Hence.log. 50 =2— x, log. 5000 = log. 500 =3- x, log. 50000 =,... | |
 | Joseph B. Mott - Algebra - 1855 - 58 pages
...equation (1), log 6 = log^ — loga; therefore, log 2 = log p — log a : a that is, the logarithm of a fraction is equal to the logarithm of the numerator, minus the logarithm of the denominator. (THEOREM 2.) Or, for a more general theorem for fractions, let us resume the equation log ^ — log... | |
 | William Smyth - Algebra - 1855 - 370 pages
...therefore by adding the logarithm of 5 to that of 7. Since moreover the logarithm of a fraction will be equal to the logarithm of the numerator minus the logarithm of the denominator, it will be sufficient to place in the tables the logarithms of entire numbers. 201. Below we have a... | |
 | Benedict Sestini - Algebra - 1857 - 258 pages
...or a*-* = - ; a* vv a" z z and consequently, x — y = I.-, that is, The logarithm of the quotient is equal to the logarithm of the numerator, minus the logarithm of the denominator. Raise to the exponent c both members of the equation a*= z, we will have (a 1 )' = z° or a" = z°,... | |
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... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. 
