...40. lo&x = -fa. 41. logs 9 = 2. 42. log, 27 = - 3. 43. log* 8 = J. Principles of Logarithms. 15. TJie logarithm of a product is equal- to the sum of the logarithms of its factors; or, logs (mxn) = logs m + Iog6n. Let log;, m = x and logj n = y ; then 61 = m and 6" = n, and therefore,...

...= l, .-. log, 1 = 0. 440. The logarithm of the base itself is 1. Proof. a1 = a, .: loga a = 1. 441. The logarithm of a product is equal to the sum of the logarithms of its factors. Proof. Let M=ax, N=a!>; then M x N= ax+». § 346 Hence loge(3f y, N) = x + y = loga M -\- log. N....

...0. For b9 = 1, or Iogb 1 = 0. 5. The logarithm of the base itself is 1. For bl = b, or Iogb&=l. 6. The logarithm of a product is equal to the sum of the logarithms of its factors ; or, Let logb m = x and logb n = y ; then b" = m and b" = n, and therefore, mn = b*b8 = b'+'/. Translated...

...rithm of 2048 to the base 2 ? Since 2048 = 32-64, we have loga 2048 = log232 + log264 = 5 + 6 = 11 7. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor; or, Iog6 (m -=- я) = logi, m - logi, л. Let logb m = x and logb...

...is 0. For ba = 1, or logj 1 = 0. 5. The loganthm of the base itself is 1. For b1 = b, or logj&=1. 6. The logarithm of a product is equal to the sum of the loejurithms of its factors ; or, Let logj m = x and logj n = y ; then b* = m and № = n, and therefore,...

...40. log2x = I15. 41. logs 9 = 2. 42. log. 27 = - 3. 43. log« 8 = \. Principles of Logarithms. 15. The logarithm of a product is equal to the sum of the logarithms of its factors; or, logi, (m X я) = logé m + logft я. Let logi та = x and logs » = У ; then bx = m and 6» =...

...For &° = 1, or log» 1 = 0. 5. The logarithm of the base itself is 1. For bl = b, or log,& = l. 6. The logarithm of a product is equal to the sum of the logarithms of its factors ; or, Let logb m = x and log5 и = у ; then b* = m and b* = n, and therefore, mn = b'b* = b'+". Translated...

...logaz = j'g. 41. log, 9 = 2. 42. log. 27 = - 3. 43. log, 8 = J. Principles of Logarithms. 15. Tlie logarithm of a product is equal to the sum of the logarithms of its factors; or, logft (mx /i) = logi, m + log(,/j. Let logb m = x and logb n = y ; then b* = m and 6» = n, and...

...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» =...

...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 +...