 | Benjamin Peirce - Algebra - 1855 - 308 pages
...Logarithm of Root, Quotient, and Reciprocal. that is, the logarithm of any power of a number is equal to the logarithm of 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,... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...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"... | |
 | Charles Davies - Algebra - 1857 - 408 pages
...definition, we have, nx' — log (N/n) ; that is, The logarithm of any power of a number is equal to the logarithm of 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 -... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...thus, (a")i=ali, and, generally, (a")m=anm. Hence, the logarithm of the power of a number is equal to the logarithm of the number multiplied by the exponent of the power. To extract the 5th root of the number a', we write a, giving it an exponent equal to f ; thus, v/as=a?,... | |
 | Charles Davies - Algebra - 1860 - 412 pages
...definition, we have, nx' — log (N'*) ; that is, The logarithm of any power of a number is equal to the logarithm of 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')*= \fW - -... | |
 | Charles Davies - Algebra - 1863 - 338 pages
...Whence, by definition, px = Log mf . . . (1.) That is, the logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. If we extract any root of both members of ( 3 ), denoted by r, we have, ar = Whence, by definition,... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...or, = log M — log N. 1o»-»=.3[ 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 10* =M, if we raise both members to the rath power, we have, 10"- = JM* Hence, log M n =... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...the definition, xp = log m r ..... (8.) That is, the loga/ithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of ( 4 ), we have, • «d' = \/m ; whence,... | |
 | Horatio Nelson Robinson - Algebra - 1872 - 436 pages
...kg. ( - J = x — я = log. m — log. я. б. — The logarithm of any power of a number ù equal to the logarithm of the number multiplied by the exponent of the power. For, let m = a" ; then x = log. m. By involution we have mr = a"; therefore, log. (mr) = rx = r log.... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...x— y is the logarithm of the quotient — . 5. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. For, raising both members of the equation ax = m to any power p, we have a?* = mP, in which xp is the... | |
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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. 
