 | 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 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' =... | |
 | 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...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... | |
 | 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 =... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...to the power denoted by p, 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...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,... | |
 | Joseph Ficklin - Algebra - 1874 - 446 pages
...subtracting the logarithm of the divisor from that of the dividend. Dividing m = a* by n = 0", 562. The logarithm of any power of a number is equal to the product of the exponent of the power and the logarithm of the number. Kaising both members of the equation... | |
 | Horatio Nelson Robinson - Algebra - 1875 - 430 pages
...= log. w. 771 By division, — = a" ; n therefore, log. I — ) = x — z = log. 7W — log. n. 5. The logarithm of any power of a number is equal to...logarithm of the number multiplied by the exponent of the power. For, let m=cf; then z = log. m. By involution, m' = a" ; therefore, log. (mr) =rx = r... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...12.234 : 87.5 X 3.7547 : : 56.5 : x, to find x. 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 the power. Let (1) bz =и; then, by def., log n =x. (1)*=(2) 6"x=n!'; then, by def., log n'—px.... | |
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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. 
