 | George Albert Wentworth - Algebra - 1881 - 406 pages
...exponents (§ 294), therefore, when roots are expressed by fractional indices, The logarithm of a root of a number is equal to the logarithm of the number multiplied by the index of the root. Thus, log 2* = \ oflog 2 = \ x 0.3010 = 0.0753. log .002* = } of (7.3010 - 10).... | |
 | Simon Newcomb - Trigonometry - 1882 - 372 pages
...of a quotient is found by subtracting the logarithm of the divisor from that of the dividend. III. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index... | |
 | Simon Newcomb - Algebra - 1882 - 302 pages
...— = 10*-*= -. Hence, by definition, A — k = los—, 9 or log p — log q = log—. THEOREM IX. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. • Proof. Let h = log p, and let n be the exponent. Then 10* — p. Raising both sides to the иth... | |
 | George Albert Wentworth - Algebra - 1897 - 536 pages
...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 oj the 2)owerFor, let x be the logarithm of m. Then то = ax, and mi' = (a?) P = aPx. .: log mP =... | |
 | James William Nicholson - Trigonometry - 1898 - 204 pages
...10«'-''. .•. (Art. 1), log( - )= a' — 6', or by (A), log f § ] = log a — log b. \°/ 4. lll. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. For, Art. 2, (/)', a* = l0"'. ... (Art. 1), logai=pa', or by (A), log a" =px loga. 5. lV. The logarithm... | |
 | Andrew Wheeler Phillips, Wendell Melville Strong - Trigonometry - 1898 - 362 pages
...dividend minus the logarithm of the divisor. Thus log»— — logam — logan. n The logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent. Thus loga m*=p loga m. To obtain the logarithm of a number to any base a from its Naperian logarithm,... | |
 | George Egbert Fisher - Algebra - 1899 - 506 pages
...1=0. Eg, Iog2 4 = 2, and Iog2 £ = — 2. 19. Tlie 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, ) = p log m. Let logj m — x, then 6* = m. Raising both sides of the last equation to the pth... | |
 | Pitt Durfee - Plane trigonometry - 1900 - 122 pages
...logarithm of the divisor. Raising m = 10* to the £th power, m1ft = 10ift*, or log mk = kx = k log m. III. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. Since a root is a fractional power, the logarithm of the kti\ root of a number is — times the logarithm... | |
 | George Egbert Fisher - Algebra - 1900 - 438 pages
...logj 1=0. Eg, log2 4 = 2, and log2 \ = — 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 =/> 1og/n. Let logj m = x, then b* = m. Raising both sides of the last equation to the pth power,... | |
 | James Morford Taylor - Algebra - 1900 - 504 pages
...log, M — log, N. Eg , log, (243 -i- 27) = log, 243 - log, 27 = 5-3 = 2. 443. The logarithm of an;/ power of a number is equal to the logarithm of the number multiplied by the exponent of tlie, power. Proof. Let M=a'; then, for all real values of p, we have M' = a'*. § 348 Hence logt(M')=px=plogaM.... | |
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The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
