 The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number by the index of the power. For let m = a"; therefore m' = (a")  Plane Trigonometry ... - Page 93by Isaac Todhunter - 1860Full view - About this book
 | Frank Castle - Mathematics - 1899 - 424 pages
...loga = .r and )ogb=y; :. a=10*, 6 = 10*. Hence = 10-' (iii) The logarithm of the power of a number is the product of the logarithm of the number by the index of the power. Let loga = #. Then a =10*. And a° =(10*)° ; .-. log,0a° = nz=n log a. The characteristic of a Logarithm.... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 512 pages
...For, logi - = logj 1 - logj n n = — logj n, since logj 1 = 0. Eg, log2 4 = 2, and log2 J = - 2. 10. The logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power; or log/n" =plogm. Let logj m = x,... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 484 pages
...- = logb 1 - logj n n = - logj n, since logb 1 = 0. .E7.gr., log2 4 = 2, and log2 \ = - 2. 10. TJie logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power ; or log m" = p log m. Let logj m =... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...log„ n — loga p. [§557, 5J ,og. (1)= = log„ 2 + log,, 3 + log„ 5 - log„ 7 — loga 11. 558. The logarithm of any power, integral or fractional,...equal to the product of the logarithm of the number and the index of the power. Thus loga (w") = n log „m. Proof. Let (1) m = a', (2) x = logam. [2555]... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...loga m — logn « — loga p. [2557, 5] ,,,g = logo 2 + logo 3 + loga 5 - loga 7 — log. 11. 558. The logarithm of any power, integral or fractional,...equal to the product of the logarithm of the number and the index of the power. Thus loga (m") = nlog(1TO. Proof. Let (1) m = a", (2) * = logam. [1555]... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 324 pages
...For, logi - = logj 1 - logj n n = — logj n, since logj 1=0. Eg, log, 4 = 2, and log2 i = - 2. 10. The logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power ; or log m" = p log m. Let logj m =... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1901 - 664 pages
...logs - = logo 1 - logs ra n = - logt, «j since logi 1=0. Eg, logs 4 = 2, and Iog2 J = - 2. 19. 27ге logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the exponent of the power; or, log (m") = p log m. Let logi m... | |
 | George Egbert Fisher - 1901 - 622 pages
...- = Iog6 1 - Iog6 n n = — logj n, since logj 1=0. E. д., Iog2 4 = 2, and Iog2 J = - 2. 10. Tlie logarithm of any power, integral or fractional, of a number is equal to the logarithm of the number multiplied by the t of the power; or log m" = p log m. Let logj m = x, then... | |
 | Ernest Smith Awmack Robson - Heat - 1902 - 212 pages
...3.1069 log b = 4.2099 .'. log a = 2.2846 log •; = 2.0747 .-. g=0.ou88 (3) The logarithm of a power is the product of the logarithm of the number by the index of the power ; or log «" = « x log a. ii Also log£/rt = loga"=-x logn. Eg (i.) log (0.005 1 26)i = 3 log 0.005... | |
 | Trinity College (Dublin, Ireland) - 1912 - 624 pages
...on the side />. 10. Prove — («) That the logarithm of I is o, whatever the base may be ; (*) That the logarithm of any power, integral or fractional,...equal to the product of the logarithm of the number and the index of the power. LOGIC. MR. EXHAM. 1. Name the various processes of Immediate Inference,... | |
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