Books Books The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 81
by Nathan Scholfield - 1845 ## A Secondary Arithmetic

John Charles Stone - Business mathematics - 1908 - 266 pages
...nf = (a°)r = a?'. Hence, log a nf = px = p logo n. IV. The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root. For let a I =?i. r,- ,v—• Then, v n=ya'=a r . EXAMPLE 1. Iogio30=logio2x3x5=log 1 o2+logio34-logi... ## High School Algebra: Complete Course

Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 520 pages
...logarithm of the dividend minus the logarithm of the divisor. (b) The logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log 2 = loga — log b and log л/о = D П EXERCISES By means of logarithms approximate the... ## Practical Calculations for Engineers, for the Use of Engineering Students ...

Charles Edward Larard, Henry Albert Golding - Engineering - 1909 - 506 pages
...the number itself multiplied by the index of the power, and also that the logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. This is the mathematical principle underlying the determination of powers and roots by means of the... ## Plane Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 276 pages
...ax. Hence, np = (a1)»1 = apx or, loga (n?) =px = p log« n. * (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga и, then n = a". Extracting the qth root of both members, we get = a«, whence, log«... ## Plane Trigonometry

Levi Leonard Conant - Plane trigonometry - 1909 - 284 pages
...the power. PROOF. mv = (10*)" = 10*y. .'. log mv = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. x PROOF. VTO = Vl& = 10". , y, — X log m .'. logvm = - = — — . yy 6. The logarithm of any integral... ## Trigonometry

Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...a*. Hence, np = (a1)" = ap* or, log« (n'») = px = p loga n. (3) IV. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. For, if x = loga n, then n = ax. Extracting the <?th root of both members, we get V71 = яi, whence,... ## Plane and Spherical Trigonometry

Levi Leonard Conant - Trigonometry - 1909 - 316 pages
...the power. PROOF. m? = (10*)" = 10*». .'. log m v = xy = y log m. 5. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. i -?/— —® — log m yy ' X 6. The logarithm of any integral power or root of 10 is an integral... ## Practical Algebra (revised) Prepared for the Use of the Midshipmen at the ...

Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...(6•)» = J~, or logs (mn) =nx. But , x = logs m; logs m n = n- log s m. VI. T^e logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let m=b x , or logsm=a;; then or n * VII. The logarithm of a proper fraction is always a negative number,... ## A Text-book on Advanced Algebra and Trigonometry, with Tables

William Charles Brenke - Algebra - 1910 - 376 pages
...of the power times the. logarithm of the number.. IV. The logarithm of any root of à number equals the logarithm of the number divided by the index of the root. (Rule III contains rule IV, since the power in question may be fractional.) 40. The following facts... 