 Whence xz is the logarithm of the zth power of m. QE D 181. 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....  Elements of Trigonometry, Plane and Spherical - Page 2by Edward Olney - 1872 - 201 pagesFull view - About this book
 | Silas Totten - Algebra - 1836 - 332 pages
...^ I. y — 1. Vy, £ \.y = 1. Vy, J \.y = 1. Vy, 1 « — \.y = \.Vy; n from which it follows, that the logarithm of any root of a number is the logarithm of the number itself divided by the index of the root. Reduction of Exponential Equations by Logarithms. (113.) If... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...10r, (N)r = (10*)' = 10" .-. rx is the Log. of (N)r ie, Log. (N) =. rx = r Log. N. 4. The Log. of the root of a number is the Logarithm of the number divided by the quantity expressing the root. For, since N = 10*, (N)? = (10 }-' = 10? /. - is the Log of (N)' /. Log.... | |
 | Paul Allen Towne - Algebra - 1865 - 314 pages
...126, ex. 20, the m* root of the equation, a" = M * m is a" = VM. That is, The logarithm of the tn"' root of a number is the logarithm of the number divided by m. Thus, the logarithm of 10000000000 is 10, and the logarithm of the 1 . 1nn • *> ftth root of 10000000000,... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...power, as the гth, we have axz — m?- Whence a» is the logarithm of the zth power of m- Q- в- D12 Prop 4:, — The logarithm of any root of a number...divided by the number expressing the degree of the notDEM Let a be the base, and x the logarithm of m- Then ax — m- Extracting the zth root we have... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...10", (N)" = (10*}' = 1o™ .'. rx is the Log. of (N)r ie, Log. (N/ = rx = r Log. N. 4. The Log. of the root of a number is the Logarithm of the number divided by the quantity expressing the root. For, since N = 10*, (N); = (10*)' = Ю' x * .-. - is the Log of (N)'... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...logarithm of то. Then ax = m ; and raising both to any power, as the ztb, we have a" = m". Whence a;z is the logarithm of the zth power of m. QED 12. Prop....Let a be the base, and x the logarithm of m. Then ax = m. Extracting the zth root we have al= \/m. Whence - is the logarithm ofVm. QED TABLE OF LOGARITHMS.... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...both to any power, as the zth, we have <*" = m*. Whence xz is the logarithm of the zth power of mq KD 12. Prop. 4:. — The logarithm of any root of a number...Let a be the base, and x the logarithm of m. Then of — m. Extracting the «th root we have af= \fm. Whence- is the logarithm ofVm. QKP TABLE OF LOGARITHMS.... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...we have 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...Let a be the base, and x the logarithm of m. Then ar=m. Extracting the 2th root we have az— ^/m. Whence - is the logarithm of ^/m. QED 182. It is evident... | |
 | Edward Olney - 1878 - 360 pages
...any power, as the zth, we have axz=m*. Whence xz is the logarithm of the zth power of m. QE D 181. Prop. 4. — The logarithm of any root of a number...Let a be the base, and x the logarithm of m. Then ax=m. Ei* tracting the uth root we have az= <\/m. Whence - is the logarithm of -у'яг. z QED 182.... | |
 | Edward Olney - Algebra - 1878 - 516 pages
...xz is the logarithm of the 2th power of m. QED 124. Prop. 4. The, logarithm of any root of a numlter is the logarithm of the number divided by the number expressing the degree of the root. DEM. — Let o be the base, and x the logarithm of m. Then ax = m. - . - x Extracting the zth root we have a* =... | |
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