 | Robert Potts - 1876 - 392 sider
...way it may be shewn that the logj«, . «, . «s . : . . } =log„«i + logA + log„Ms + . . . . Or that the logarithm of the product of any number of factors, is equal to the sum of the logarithms of the several factors. 3. PROP. To find the logarithm of the quotient of two numbers. Here «! = alos«1ti,... | |
 | Webster Wells - 1878 - 124 sider
...of zero is minus infinity. For, since er"0 = — = — = 0, — oo = loga 0. rf" 12* In any system, the logarithm of the product of any number of factors,...equal to the sum of the logarithms of those factors. Assume the equations, a* — m \ т, i, < . i } ж — loga m „ t whence, by Art. 1,1 , a" = n )... | |
 | Webster Wells - 1879 - 468 sider
...— 00 = loga 0. a oo If the base is less than unity, the logarithm of 0 is + op . 455. In any system the logarithm of the product of any number of factors...equal to the sum of the logarithms of those factors. Assume the equations, a" — m) > •• / , .: > > (x = 1огa m \ whence, by Art. 444, >. , 8" an... | |
 | John Charles Snowball - 1880 - 256 sider
...connecting the logarithms of a number in the two systems whose bases are a and e, is ^ — . L» 4. The logarithm of the product of any number of factors is equal to the sum of the logarithms of the several factors. For m.».r...=aUm.a1'"t.a1»í-...=íl(1»mH""+Ur+-) But m.».r...=a1"("wr-);... | |
 | Webster Wells - 1883 - 298 sider
...less than unity, the logarithm of 0 is +00. For since, when a<l, o"= 0, oo =loga0. 95. In any system the logarithm of the product of any number of factors...equal to the sum of the logarithms of those factors. Assume the equations whence, by Art. 84, Multiplying, a" X a* X a• X •-• = mnp • •• That... | |
 | Daniel Alexander Murray - 1899 - 226 sider
...the properties, or are the laws of logarithms. They may be expressed in words as follows : (1) Tlie logarithm of the product of any number of factors is equal to the sum of the logarithms of the factors. (2) Tlie logarithm of the quotient of two numbers is equal to the logarithm of the numerator... | |
 | James Morford Taylor - 1900 - 504 sider
...power of any base is equal to the mnth power of that base. That is, (am)" = amn. Ill TJie nth power of the product of any number of factors is equal to the product of the nth powers of the factors. The nth power of the quotient of one number by another is... | |
 | Louis Parker Jocelyn - 1902 - 460 sider
...the numerator of a fractional exponent indicates a power, and the denominator a root. 2. The wth root of the product of any number of factors is equal to the product of the wth roots of those factors ; that is, N/a'V/V' ••• = лУа" • \/¿" • л/с"... | |
 | Daniel Alexander Murray - 1906 - 466 sider
...state the properties, or are the laws of logarithms. They may be expressed in words as follows : (1) The logarithm of the product of any number of factors is equal to the sum of the logarithms of the factors. (2) The logarithm of the quotient of two numbers is equal to the logarithm of the numerator... | |
 | Constantine Kenneth Smoley - 1906 - 366 sider
...use of the Log・ tables is based upon the fol1owing four properties of 1ogarithms: (1) The Log・ of the product of any number of factors is equal to the sum of the Logs, of these factors・ Accordingly, multipli cation can be effected by adding the Logs, of the given... | |
| |
Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence... 
