| William Smyth - Algebra - 1851 - 272 pages
...= N, or, raising both members to the mth power, ami= Nm; whence the logarithm of Nm= mx = m log. N. **That is, the logarithm of any power of a number is equal to the** prodiut of the logarithm of this number by the exponent of the power. To raise a number, therefore,... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...10mX"=Mn, in which m X n is the logarithm of M n (Art. 1) : hence, The logarithm of any power of a given **number is equal to the logarithm of the number multiplied by the exponent of the power.** 16. Taking the same equation, IQ™=M, and extracting the nib. root of both members, we have m _! 10n=ifn'... | |
| Charles Davies - Geometry - 1854 - 436 pages
...WmXn=M", in which m X n is the logarithm of J/" (Art. 1) : hence, The logarithm, of any power of a given **number is equal to the logarithm of the number multiplied by 'the exponent of the power.** 16. Taking the same equation, 1Om = M, and extracting the nth root of both members, we have HI which... | |
| Benjamin Peirce - Algebra - 1855 - 308 pages
...all equal to each other, we have log. mmm &c. = log. m .\. log. m -}- log. m -j- &c. or log. mn r= n **log. m ; Logarithm of Root, Quotient, and Reciprocal....the number multiplied by the exponent of the power.** 12. Corollary. If we substitute p — ran, in the above equation, it becomes log. p = n log. v/ p,... | |
| Joseph B. Mott - Algebra - 1855 - 58 pages
...log a ; T —Y and if n = -, then losam = - losa : m ° m that is, the logarithm of any power or root **of a number is equal to the logarithm of the number multiplied by the exponent** ....... , ------ ----------- --------- (THEOREMS.) 1. log 81 = log 34 = 4 log 3 = 4X. 477121 = 1.908484.... | |
| Elias Loomis - Algebra - 1855 - 356 pages
...have log. 20 =x+l, log. 20000 = log. 2000=a;+3, log. 2000000=, &c. We have seen, in Art. 340, that **the logarithm of any power of a number is equal to the logarithm of** that number multiplied bv the exponent of the power. Hence, log. 4 =2x, log. 32 = log. 16=4a;, log.... | |
| Elias Loomis - Trigonometry - 1855 - 192 pages
...-0.4753 divided by —36.74. INVOLUTION BY LoGARITHMS. (14.) It is proved in Algebra, Art. 340, that **the logarithm of any power of a number is equal to the logarithm of** that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we have... | |
| William Smyth - Algebra - 1855 - 370 pages
...raising both members to the rath power, we have a^ = ym; ' whence the logarithm of ym = mx = m log y. **That is, the logarithm of any power of a number is equal to the** product of the logarithm of this number by the exponent of the power. To form any power whatever of... | |
| Charles Davies - Algebra - 1857 - 408 pages
...(1) to the «'* power, we have, a*.' = N'n (5). But from the definition, we have, nx' — log (N/n) ; **that is, The logarithm of any power of a number is...the number multiplied by the exponent of the power.** 233. If we extract the nth root of both members of equation (1), we shall have, , a" -(N')~n- *JW -... | |
| Adrien Marie Legendre - Geometry - 1857 - 444 pages
...10mXn=J/n, in which m X n is the logarithm of M * (Art. 1) : hence, The logarithm of any power of a given **number is equal to the logarithm of the number multiplied by the exponent of the power.** 16. Taking the same equation, W'" = M, and extracting the nth root of both members, we have m _. 10"... | |
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