 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
 | George Darley - 1835 - 142 pages
...to the difference of their logarithms, 7ART. 5. The logarithm of the power of any number is equal to the logarithm of the number multiplied by the index of the power, 8. AHT. 6. The logarithm of the root of any number is equal to the logarithm of the number divided... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...to base a, or (as we usually write it) x + y = loga NN' ; In like manner N 123. The logarithm of any power of a number is the logarithm of the number multiplied by the index which expresses the power. Suppose a= = N, then a?' = Np, or px = logaJV by definition, but x = loga... | |
 | Barnard Smith - 1857 - 740 pages
...log.(.ZViV,)=log..ZV+log..ZV,. N , Again, jj =<?->; (N\ — J =xy, by definition, 202. The logarithm of any power of a number is the logarithm of the number multiplied by the index which expresses the power. As in last Art. let N=a". Then N" = a"x; •'. loga( TV*") =px, by definition... | |
 | Thomas Kimber - Mathematics - 1865 - 302 pages
...what precedes — log., i = log.. 1 — log.. N, = 0 - log.. N, = - log.. N. 6°. The logarithm of any power of a number, is the logarithm of the number multiplied by the index which expresses the power. Suppose of = N, then a'' = TV», or vp = log.. N' by definition ; but p... | |
 | Richard Wormell - Arithmetic - 1868 - 184 pages
...example, the log. of (144 -_ 16) = log. of 144 — the log. of 16. 3. The logarithm of the power of any number, is the logarithm of the number multiplied by the index of the power. For example, the log. of (54) = 4 times the log. of 5. 4. The logarithm of the root of any number is... | |
 | Arthur Stokes - Trigonometry - 1868 - 170 pages
...logal - loga oo = oo (by Art. 89). 91. To shew that the logarithm of a number to any power is equal to the logarithm of the number, multiplied by the index of the power, ie log„(mr) = r log„m. , Let log„n» = x, a" = m, a" = m', whence loga(mr) = xr = r log„m.... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...n- Dividing, we have a*-» = —- Wheuce z — у is the logarithm of n it <)- E- D11- Prop- 3- — The logarithm of a power of a number is the logarithm of the number multiplied by the index of the powerDK,W Let a be th e base, and x the logarithm of m- Then of — m ; and raising l)oth to any power,... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...n. Dividing, we have ax~v = — . Whence x — y is the logarithm of — n n' QED 11. Prop. 3. — The logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DKM. Let a be the base, and x the logarithm of то. Then ax = m ; and raising both to any power, as... | |
 | Edward Olney - Trigonometry - 1872 - 216 pages
...я. Dividing, we have a*-' = — . "Whence x — y is the logarithm of ~, q. ED 11. Prop. 3. — Tlie logarithm of a power of a number is the logarithm...of the number multiplied by the index of the power. DEM. Let я be the base, and z the logarithm of m. Then a* = m ; and raising both to any power, as... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...Dividing, we have a1-» — —. Whence x — y is the logarithm . m of — . q. 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 m. Then az=m ; and raising both to any power, as... | |
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