 | Benjamin Greenleaf - Algebra - 1879 - 350 pages
...= n, and dividing, member by member, we have in which x — y = log,, ( — )• 360. The logarithm of any power of a number is equal to the logarithm...the number, multiplied by the exponent of the power. For, assume the equation, cf =m, and raising both members to the power p, we have axP = m?, in which... | |
 | Benjamin Greenleaf - 1879 - 346 pages
...ai — n, and dividing, member by member, we have in which x — y = loga ( —V 360. The logarithm of any power of a number is equal to the logarithm...the number, multiplied by the exponent of the power. For, assume the equation, of =zm, and raising both members to the power p, we have <ff = mp, in which... | |
 | Benjamin Greenleaf - Algebra - 1879 - 322 pages
...member, we have in which x — y = logn ( — Y 360. The logarithm of any power of a number is equnl to the logarithm of the number, multiplied by the exponent of the power. For, assume the equation, dc = m, and raising both members to the power p, we have ax" = mP, in which... | |
 | 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...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, 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).... | |
 | Henry Nathan Wheeler - Logarithms - 1882 - 60 pages
...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 logarithm...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 - Logarithms - 1882 - 204 pages
...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 logarithm...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... | |
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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. 
