| 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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