| Robert Potts - 1876
...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 - 96 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 - 444 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
...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
...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
...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 - 461 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 - 445 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"... | |
| 1906
...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 - 332 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... | |
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