 | James Hamblin Smith - Trigonometry - 1870 - 286 pages
...1-7191323 their difference = -8508148 which is the logarithm of 7-092752, the quotient required. 146. The logarithm of any power of a number is equal to the product of the logarithm of the number and the index denoting the power. Let m = a'. Then m' = a";... | |
 | 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...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.... | |
 | Daniel Barnard Hagar - Algebra - 1873 - 278 pages
...equation a" = n, member by 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 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 - 506 pages
...12.234 : 87.5 X 3.7547 : : 56.5 : j, to find x. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to...the number multiplied by the exponent of the power. Let (1) b' =n; then, by def., log n = x. (1)»=(2) bp'=np; then, by def., log np=px. . . . log np =... | |
 | Aaron Schuyler - Measurement - 1864 - 512 pages
...12.234 : 87.5 X 3.7547 : : 56.5 : r, to find z. Ans. 2014.96. INVOLUTION BY LOGARITHMS. 22. Proposition. The logarithm of any power of a number is equal to...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
...if»>m, loga is negative, 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... | |
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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. 
