| John Bonnycastle - 1848
...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—... | |
| JAMES RYAN - 1851
...Q% If ' down in the first part of this article, x — x' = log. -, or log. 2. = log. y - log. y'. y **Hence, the logarithm of a fraction, or of the quotient...denominator. And if each member of the common equation** a? — y be raised to the fractional power denoted by — , we shall have, m —x in that case, a n... | |
| Joseph Ray - 1852 - 396 sider
...logarithm of the quotient. The same principle may be expressed otherwise thus, the logarithm of a fraction **is equal to the logarithm of the numerator, minus the logarithm of the denominator.** From this article, and the preceding, we see that by means of logarithms, the operation of Multiplication... | |
| Elias Loomis - 1855 - 316 sider
...equal to ^ ; hence, PROPERTY II. The logarithm of a fraction, or of the quotient of one number divided **by another, is equal to the logarithm of the numerator, minus the logarithm of the denominator.** Hence we see that if we wish to divide one number by another, we have only to subtract the logarithm... | |
| JOSEPH B. MOTT. - 1855
...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 - 1855 - 336 sider
...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 - 1857 - 216 sider
...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°,... | |
| Charles Davies - 1857 - 400 sider
...definition, v , (N' \ , • of — x" = log I -— 1 ; that is, The logarithm of the quotient which arises **from dividing one number by another is equal to the logarithm of the** dividend minus the logarithm of the divisor. 232i If we raise both members of equation (1) to the «'*... | |
| William Smyth - 1858 - 320 sider
...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... | |
| Charles Davies - 1860 - 400 sider
........ w J5ut, from the definition. (N' \ -]yr)-> that is, The logarithm of the quotient which arises **from dividing one number by another is equal to the logarithm of the** dividend minus the logarithm of tin divisor. 232t If we raise both members of equation (1) to the nth... | |
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