 | Robert Potts - 1876 - 418 σελίδες
...«logc" by def. Then raising each to the »ih power. a• = a-dogi«. .•. loga{«•} = n loga«. Or, the logarithm of any power of a number, is equal to the product of the logarithm of the number and the index of the power. 5. PEOP. To find the logarithm of... | |
 | Edward Brooks - 1877 - 564 σελίδες
...by the second, we have, »•— f Hence, log ( — J = m — n, or, = log M — log N. PRIN. 6. — The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, since if we raise both members to the nth... | |
 | Elias Loomis - 1879 - 398 σελίδες
...corresponding to the resulting logarithm, and it will be the quotient required. 398. Tlte logariOim of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. If we raise both members of Eq. (1) to any power denoted by ]), we have apx=mp.... | |
 | Benjamin Greenleaf - 1879 - 376 σελίδες
...equations, ax = m, a" = n, and dividing, member by member, we have , „ in ax~>> — — n (V »/' 3fiO. The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the exponent of the power. For, assume the equation, a* = m, and raising... | |
 | Benjamin Greenleaf - 1879 - 346 σελίδες
...equations, a* = wi, 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 of the number, multiplied by the exponent of the power. For, assume the equation, of =zm, and raising... | |
 | William Findlay Shunk - 1880 - 362 σελίδες
...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 logarithm of the number multiplied by the exponent of the power. The logarithm of any root of a number is equal... | |
 | B. Greenleaf - 1880 - 320 σελίδες
...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 logarithm of the number, multiplied by the exponent of the power. For, assume the equation, ax = m, and raising... | |
 | Elias Loomis - 1881 - 398 σελίδες
...corresponding to the resulting logarithm, and it will be the quotient required. 398. The logariihm of any power of a number is equal to the logarithm of Hiat number multiplied by the exponent of the power. If we raise both members of Eq. (1) to any power... | |
 | Henry Nathan Wheeler - 1882 - 60 σελίδες
...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 logarithm of the number multiplied by the exponent of the power. Proof: If I = 6х, then is log6Z = ж, lm = (b*)"1... | |
 | Simon Newcomb - 1882 - 302 σελίδες
...— = 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 logarithm of the number multiplied by the exponent of the power. • Proof. Let h = log p, and let n be the exponent.... | |
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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. 
