 The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. log» Np = p log  Elementary Algebra - Page 277by Walter William Rouse Ball - 1890 - 486 pagesFull view - About this book
 | Andrew Bell (writer on mathematics.) - 1839 - 500 pages
...logarithms.1 For ax -=- a* = - or e"' = -; and hence x — ж'= l ~, У У1 У' or l?L = ly — ty (503.) ' The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power.1 If ax = y, then а«.т = yn ; and... | |
 | John Clement P. Aldous - 1874 - 104 pages
...difference of the logarithms of the factors, as Iog105=log1010-log102. 3. The logarithm of a power is equal to the product of the index of the power, and the logarithm of the number, as • Ioglo32 = 21og103. 77 Tables are computed which give the logarithms of numbers, and the logarithms... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1881 - 446 pages
...16. log 7.5. 24. log 37.5. 32. log 1.05. 412. As logarithms are simply exponents, therefore (§ 381), The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Thus, Iog57 = 7 x log 5= 7x0.6990... | |
 | George Albert Wentworth - Algebra - 1881 - 400 pages
...From this it follows that log — = log 1 — log m. But, since log 1 = 0, log - = — log m. III. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, let x be the logarithm of m.... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...the m lb power, N ™ = &™* whence it appears (Art. 384) that mx is the logarithm of N m . Hence The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 394. To find the logarithm of a root.... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...log 7.5. 24. log 37.5. 32. log 1.05. C 412. As logarithms are simply exponents, therefore (§381), The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Thus, log 5' = 7 X log 5 = 7 X 0.6990... | |
 | George Albert Wentworth - Arithmetic - 1888 - 392 pages
...16. log 7.5. 24. log 37.5. 32. log 1.05. 412. As logarithms are simply exponents, therefore (§ 381), The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Thus, log 5' = 7 X log 5= 7x0.6990... | |
 | Charles Ambrose Van Velzer, Charles Sumner Slichter - Algebra - 1888 - 234 pages
...Therefore, by definition, , f«l 10g,, -| or, by equation (i), .<,. = log,, n— log,,,/-. 9. THEOREM. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Let n be any number, and let log,,«... | |
 | William James Milne - Algebra - 1901 - 476 pages
...Involution by logarithms. Since logarithms are simply exponents, it follows that: 472. PRINCIPLE. — The logarithm of a power of a number is equal to the logarithm of the number multiplied by the index of the power; that is, To any base, bg m" = n log m.... | |
 | John Marvin Colaw - Algebra - 1903 - 444 pages
...18 3245 x .7246 20 -- 400 x .005 3.24 -s- 65 4.9 x(-306) x 48.3 6.32 x 7832' 100 x 2.9 x .081 481. The logarithm of a power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Thus, 100" = (102)3 = 102*3 = 106.... | |
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