 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...ar» exponent equal to 3x5; 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?,... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...of (4) to the power denoted by JP, we have, whence, by the definition, xp = log mp (8.) That is, the logarithm of any power of a number is equal to the logarithm of tJie number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both... | |
 | Benjamin Greenleaf - Algebra - 1864 - 420 pages
...equation by the second, member by member, we have Therefore, log TT = * ~~ y ~ log m — log ». 401 1 The logarithm of any power of a number is equal to the...the number multiplied by the exponent of the power. For, let m = ax ; then, raising both members to the rth power, we have mr = (<f)r = a*". Therefore,... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...second, we have, .Zv Hence, log ( — J = m — n, or, = log M — log N. 1o»-»=.3[ PRIN. 6. — The logarithm of any power of a number is equal to the...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, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...power denoted by p, we have, l01* = mp ; whence, by the definition, xp = log mr ..... (8.) That is, the logarithm of any power of a number is equal to the...the number multiplied by the exponent of the power. 8. Extracting the root, indicated by r, of both members of (4), we have, whence, by the definition,... | |
 | Charles Davies - Leveling - 1871 - 448 pages
...power denoted by t, we have, l0* = m'; whence, by the definition, pt = log m, ....... (8.) That is, the logarithm of any power of a number, is equal to the...logarithm of the number multiplied by the exponent of Ike power. 8. Extracting the root, indicated by r, of both members of (4), we have, 1CT = ym; whence,... | |
 | Elias Loomis - Geometry - 1871 - 302 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... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...denoted by p, we have, = m r whence, by the definition, xp = log m r ..... (8.) That is, the loga/ithm of any power of a number is equal to the logarithm...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
...therefore, 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.... | |
 | Aaron Schuyler - Measurement - 1873 - 508 pages
...87.5 X 3.7547 : : 56.5 : x, to find x. Am. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the...the number multiplied by the exponent of the power. Let -(1) b* =n; then, by def., log n =x. (1)"=(2) b"*=n"; then, by def., log n"=jpx. . • . log n"... | |
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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. 
