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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.
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 75
by Nathan Scholfield - 1845

Plane Trigonometry

Elmer Adelbert Lyman, Edwin Charles Goddard - Plane trigonometry - 1899 - 188 pages
...equals the index of the power times the logarithm of the number. IV. The logarithm of a root equals the logarithm of the number divided by the index of the root. For if ax = n and av = m, then nxm = ax+v, .•. logwm = x + y = logn + logm; and n .t. m = ax~v, .'.log—...

Elements of Algebra with Exercises

George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 506 pages
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. ,ir For, logi (m') = llog m = Ч Ч Eg, If Iog7 2401 = 4, what is Iog7 V2401 ? We have Iog7 V2401 =...

Elements of Algebra

James Morford Taylor - Algebra - 1900 - 504 pages
...logarithm of the number multiplied by the exponent of the power ; and the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. Ex. 1. Given Iog102 = . 30103 and Iogi03 = .47712 ; find Iog10^/720. logio -У720 = J Iog10 (2s x 32...

Plane and Spherical Trigonometry

Elmer Adelbert Lyman, Edwin Charles Goddard - Trigonometry - 1900 - 228 pages
...equals the index of the power times the logarithm of the number. IV. The logarithm of a r00t equals the logarithm of the number divided by the index of the root. For if a* = n and a" = m, then nxwI = a•"~", ... log nm = x + y = log n + logra; and n •+• m...

Secondary Algebra

George Egbert Fisher, Isaac Joachim Schwatt - Algebra - 1900 - 484 pages
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. For, lo E. д., If log, 2401 = 4, what is log7 We have log, л/2401 = \ log, 2401 =1-4 = 2. 2 2¡ 416...

College Algebra

James Harrington Boyd - Algebra - 1901 - 818 pages
...COROLLARY. —Put n — - for n in (5), then (6) loga (mr) = ;loga"*That is, ?Ae logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Kg., 559. It follows from (5), (6), and (7) that by the use of logarithms the operations of multiplication...

William James Milne - Algebra - 1901 - 462 pages
...logarithms are simply exponents, it follows that : 474. PRINCIPLE. — The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the required root; that is, , „,- log m lo any base, log vm = The above principle may be established...

Complete Secondary Algebra

George Egbert Fisher - 1901 - 320 pages
...numerator is 1, this principle may be conveniently stated thus : The logarithm of a root of a number is the logarithm of the number divided by the index of the root. For, lo Eg, If logr 2401 = 4, what is log, V2401 ? We have log, д/2401 = - log, 2401 = - . 4 = 2....