 Whence x — y is the logarithm m of — . QED n 180. Prop. 3. — The logarithm of a power of a number is the logarithm of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m.  High School Algebra: Advanced Course - Page 173by Herbert Ellsworth Slaught, Nels Johann Lennes - 1908 - 194 pagesFull view - About this book
 | Charles Elsee - 1873 - 320 pages
...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 = m lnga я. Since m may... | |
 | Edward Olney - Algebra - 1877 - 466 pages
...Dividing, we have a? ~ » = — . Whence x — y is the logarithm of — . Q. K . ». 123. Prop. 3. The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m. Then a1 = m ; and raising both to any power,... | |
 | Edward Olney - Algebra - 1878 - 516 pages
...= n. Dividing, we have a* — * = — . Whence x — y is the logarithm of — . QED 123. Prop. 3. The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM.— Let a be the base, and a; the logarithm of m. Then a* = m ; and raising both to any power,... | |
 | Edward Olney - 1878 - 360 pages
...и. Dividing, we have a*-* = — . Whence x — y is the logarithm m of — . QED n 180. Prop. 3. — The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m. Then a'=m ; and raising both to any power, as... | |
 | Edward Olney - Algebra - 1880 - 354 pages
...Dividing, we have a*—' = —. Whence x — y is the logarithm . m of — . о. ED n 180. Prop. 3. — The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of то. Then a*=m ; and raising both to any power,... | |
 | Edward Olney - Algebra - 1881 - 504 pages
...Dividing, we have a*-* = —. Whence x— y is the logarithm of — . QED n ' n 123. Prop. 3. — Tlie logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. Demonstration. — Let a be the base, and x the logarithm of m. Then a1 — m • and raising both... | |
 | Edward Olney - Algebra - 1882 - 358 pages
...Dividing, we have a*~> = — . Whence x — y is the logarithm . m Of — . «JED 180. Prop. 3. — The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m. Then a'=m ; and raising both to any power, as... | |
 | Robert Hamilton Pinkerton - Trigonometry - 1884 - 194 pages
...positive or negative, of a number — the root of a number being considered as a fractional power — is the logarithm of the number multiplied by the index of the power. The proofs of these properties follow very easily from the definition of the logarithm of a number... | |
 | Edward Olney - Algebra - 1885 - 364 pages
...Dividing, we have a1—* = — . Whence x — y is the logarithm . »> Of — . QED 180. Prop. 3. — T/te logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. — Let a be the base, and J the logarithm of m. Then a'=m ; and raising both to any power, as... | |
 | Algebra - 1888 - 492 pages
...and y. Then, by definition, we have a" = m. and «' = n. Dividing, we have 41Í). PKIÎÎ. III. — The logarithm of a power of a number is the logarithm of the number multiplied hy the index of the power. Let a bo the base, and x the logarithm of m. Then (f = m ; and raising both... | |
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