| 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"; .-. log m' = rx = r . log„«i. Thus the... | |
| Isaac Todhunter - Algebra - 1870 - 626 pages
...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' = (a*)r = a**, therefore loga (mr) = XT =... | |
| Charles Davies - Surveying - 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... | |
| 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,... | |
| Charles Elsee - 1873 - 318 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*, . •... | |
| 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 the logarithm of the number multiplied by the exponent of thc power. Let (1) b* =n; then, by def., 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 logarithm of the number multiplied by the exponent of the power. For, raising both members of the equation... | |
| Mechanical engineering - 1874 - 1186 pages
...whence, by the definition, log. ym=m .•=//' log. y ; that is, the logarithm of the power of a number ia equal to the product of the logarithm of the number by the exponent of the power. If in the equation of log. y™ = m log. y we make m = -, we shall have log. y* (or log. */ y) = —... | |
| 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 m = a*... | |
| Isaac Todhunter - Plane trigonometry - 1874 - 360 pages
...therefore loga -=x — y = logam - Iog0w. 137. 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. Por let »i = a' ; therefore mr = (a')' = a", therefore loga (mr) = rx... | |
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