 | William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...quotient is equal to the logarithm of the dividend diminished by that of the divisor. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index... | |
 | Horatio Nelson Robinson - Trigonometry - 1880 - 228 pages
...exponent equal to 3x5; thus, (a i ) i = a 1 i, and, generally, (a") m =a nm . Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the pmver. To extract the 5th root of the number a1, we write a, giving it an exponent equal to f; thus,... | |
 | Stephen Roper - Steam engineering - 1880 - 84 pages
...power of a given number may be found by logarithms as follows : The logarithm of any power of a given number is equal to the logarithm of the number multiplied by the exponent of the power. EXAMPLE.— To find the fifth power of 9, logarithm 9 = 0-954243X5 = 4-771215, and the number corresponding... | |
 | 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...the number multiplied by the exponent of the power. For, let x be the logarithm of m. Then m = an, and mP = (an)p = of. .-.log mi> = px, IV. The logarithm... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1881 - 446 pages
...0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§381), 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* = i of log 2 = £ x 0.3010 = 0.0753. log .002* = J of (7.3010 - 10).... | |
 | 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).... | |
 | 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...the number multiplied by the exponent of the power. 394. To find the logarithm of a root. Let N=b*. Taking the n" root, i/N= b", whence it appears (Art.... | |
 | Simon Newcomb - Algebra - 1882 - 302 pages
...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 logarithm of 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... | |
 | Henry Nathan Wheeler - Logarithms - 1882 - 60 pages
...Iogw123 = 2.0899 ; what is Iog100.123?_ Ans. 2.0899-3 = 1.0899. § 8. In any system the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. Proof: If I = 6х, then is log6Z = ж, lm = (b*)"1 = b™ ; .•. logZ** = mx = mx log Z. Under this... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1882 - 376 pages
...0.4771 = 5.2481. 413. As logarithms are simply exponents, therefore (§381), 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 2J = | of log 2 = } X 0.3010 = 0.0753. log .002* = J of (7.3010 - 10).... | |
| |
The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 
