...base is 1. Dem. 1. a1 = a. 2. .-. logea = l. ILLUSTRATION. 101 = 10, .-. Iog1010 = l. 467. Prop. 3. The logarithm of a product is equal to the sum of the logarithms of its factors. Dem. Let mn be the given product, and m and n the factors of the product ; then logu mn = Iog0 m +...

...40. \о&х = -^. 41. log« 9 = 2.- 42. log, 27 = - 3. 43. log., 8 = \. Principles of Logarithme. 15. The logarithm of a product is equal to the sum of the logarithms of its factors; or, logi, (mx я) = logé m + log;, я. Let logt m = x and Iog6 n = у ; then Ъ* = то and Ь» =...

...unity, a number approaches the limit 0, its logarithm increases without limit. 589. In any system, the logarithm of a product is equal to the sum of the logarithms of its factors. Assume the equations a' = m, a'— n. Then, by § 580, x = log. m, y = log„ n. Multiplying the assumed...

...hence x = 0. 5. The logarithm of the base is 1. Let x = logb b, then 6х = b, hence x = 1. 6. 37ie logarithm of a product is equal to the sum of the logarithms of its factors. Ie if logbm = x,andlogbn = y, (1) then logj, mn = x + y. (2) Writing these equations in the exponential...

...of exponents, and from these are derived the fundamental principles of logarithmic calculation : ( 1 ) The logarithm of a product is equal to the sum...the logarithms of its factors. (2) The logarithm of the quotient of two numbers is equal to the logarithm of the dividend less the logarithm of the divisor....

...= 1, hence x = 0. 5. The logarithm, of the base is 1. Let x = logj b, then b" = b, hence ж = 1. 6. The logarithm of a product is equal to the sum of the logarithms of its factors. Ie if logb m = x, and logb n = y, (1) then logj mn =*x + y. (2) Writing these equations in the exponential...

...If = 1, hence x = 0. 5. The logarithm of the base is 1. Let x = logj b, then b* = b, hence x = 1. 6. The logarithm of a product is equal to the sum of the logarithms of its factors. Ie if logb m = x, and logb n = y, (1) then logj mn = x + y. (2) Writing these equations in the exponential...

...attached to such a result as loga 0 = — no ; it must be interpreted as follows : 421. In any system, the logarithm of a product is equal to the sum of the logarithms of its factors. Assume the equations a ~ m 1 ; whence, by § 412, a* = n J Multiplying the assumed equations, a* x...

...attached to such a result as Iog00 =— oo ; it must be interpreted as follows : 421. In any system, the logarithm of a product is equal to the sum of the logarithms of its factors. Assume the equations a* = m } ; whence, by § 412, fx = lo^ ™» a»=n }' b = log.n. Multiplying the...

...said to form a system of common logarithms or Briggs logarithms. 451. From § 449 it is evident that : The logarithm of a product is equal to the sum of the logarithms of the factors. The logarithm of a quotient is equal to the logarithm of the dividend less that of the...