| 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 - 352 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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