 | John Bonnycastle - 1848 - 334 sider
...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—... | |
 | John Bonnycastle - 1851 - 288 sider
...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 - 408 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 - 356 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 - 58 sider
...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 - 370 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 - 258 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 - 408 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 - 344 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 - 412 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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N .•. def. (2), x— x1 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 (1) to... 
