 | Isaac Todhunter - Algebra - 1870 - 626 pages
...n = a? ; ma!° therefore — = — = a"-" ; no? therefore Iog0 - =x — y = logam — logan. n 537. The logarithm of any power, integral or fractional, of a number is equal to the product of the logarithm of the number and t/ie index of the power. For let m = a'; therefore m' =... | |
 | Charles Davies - Leveling - 1871 - 448 pages
...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,... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...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 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
...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
...: x, to find x. Am. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the logarithm of 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"... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...member, we have in which 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... | |
 | Aaron Schuyler - Measurement - 1864 - 512 pages
...: r, to find z. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of thc power. Let (1) b* =n; then, by def., log n =z. (1)'=(2) b'*=n'; then, by def., log n'=px. . •... | |
 | Charles Elsee - 1873 - 320 pages
...ie the logarithm of a number less than unity is negative. 160. — PROP. The logarithm of any power of a number is equal to the logarithm of the number, multiplied by the index of the power. For if x = log . га, я = о*, . • . nm = a1"* . • . loga (я™) = mx =... | |
 | Aaron Schuyler - Navigation - 1873 - 536 pages
...2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is egual to the logarithm of the number multiplied by the exponent of the power. Let (1) b• =n; then, by def., log n =x. (1y=(2) b"=n'; then, by def., log n'=p . • . log n' = p... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...we have, 10'' = mr ; whence, by the definition, xp = log mr (8.) 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. 8. Extracting the root, indicated by r, of both members of (4), we have, 10r = whence, by the definition,... | |
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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. 
