 | William Findlay Shunk - Railroad engineering - 1880 - 362 pages
...logarithm of a 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 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... | |
 | B. Greenleaf - 1880 - 320 pages
...dividing, member by member, we have wi с?-у = — n in which x — y = log. ( - )• 3(íO. TJie logarithm of any power of a number is equal to the...the number, multiplied by the exponent of the power. For, assume the equation, ax = m, and raising both members to the power p, we have аггР_ОТР,... | |
 | 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 - 402 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).... | |
 | George Albert Wentworth, Thomas Hill - Arithmetic - 1881 - 444 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).... | |
 | Henry Nathan Wheeler - 1882 - 60 pages
...0.1761. m Given: 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 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... | |
 | 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 - 304 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... | |
 | Edwin Pliny Seaver, George Augustus Walton - Algebra - 1881 - 304 pages
...™ = &™* 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. Let N=b*. Taking the n" root, i/N= b", whence it appears (Art.... | |
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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. 
