 | Edward Olney - Trigonometry - 1872 - 216 pages
...= 7»'. Whence xz is the logarithm of the zth power of m. QED 12. Prop. 4. — The logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM Let a be the base, and x the logarithm of m. Then a*... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...; whence, by the definition, ~ .... (9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. TABLE OB LOGARITHMS. 9. A TABLE OF LOGARITHMS, is a table containing a set of numbers and their logarithms,... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...агг=тг. Whence xz is the logarithm of the zth power of m. QE D 181. Prop. 4. — Tlie logarithm of any root of a number is the logarithm of the number divided by the number expressing the degree of the root. DEM. — Let a be the base, and x the logarithm of m. Then... | |
 | Aaron Schuyler - Measurement - 1864 - 506 pages
....59047. EVOLUTION BY LOGARITHMS. 25. Proposition. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let (1) b- = n; then, by def., log n = x. lX(l) = (2) b'r —1/n; then, by def., log 1</~^, = — .... | |
 | Charles Elsee - 1873 - 320 pages
...considered fractional ( = - J, we have also ^ = 7 1ов.». ic the logarithm of a root is equal to the logarithm of the number, divided by the index of the root. 161.— PROP. Logawi = Log,,™ x Logai. For let logb m = y, and log„ Ь = z, then m = Ъ", Ь =... | |
 | Mechanical engineering - 1874 - 1186 pages
...y* (or log. */ y) = — log. y ; that is to say, the logarithm of any root of a number ia equal to the logarithm of the number divided by the index of the root. From these two last results it is obvious that by means of a table of logarithms numbers may be raised... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...definition, * = log 'Jm. ' • • • ( 9.) That is, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. The preceding principles enable us to abbreviate the oper ations of multiplication and division, by... | |
 | William Guy Peck - Algebra - 1875 - 348 pages
...tfm .... (8) hence, the following principle: 4°. Tlie logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. The applications of the above principles require a table of logarithms. A table of logarithms, is a... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
....59047. I EVOLUTION BY LOGARITHMS. f 25. Proposition. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Let (1) b' = n; then, by def., log n = x. V(l) = (2) br =\/n; then, by def., log Vх n = — • r.... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
.... Therefore, log (M m) = xm = (log M) X »»12. The logarithm of the ROOT of any number is equal to the logarithm of the number divided by the index of the root. For, let n be any number, and take the equation (Art. 9) M=a*, then, extracting the nth root of both... | |
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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. 
