 | Frederick Howland Somerville - Algebra - 1908 - 428 pages
...log m, , (Art. 438) Hence, log m" = pQog "0 • 456. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the root. Let 10« = m. (1) Raising both members to the power indicated by -, x 1 9 10« = m«. •1 Whence,... | |
 | 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... | |
 | Webster Wells - Algebra - 1908 - 456 pages
...ap*—иlp. whence, Iog„mp=px=j9logam. 90. In any system, the logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. — - 1 For, log„Vm = lo&,(m;)=~ logam(§ 89). 91. Examples. 1. Given log 2 = .3010 ; find log 2Í... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 272 pages
...(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«... | |
 | Levi Leonard Conant - Trigonometry - 1909 - 320 pages
...= (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... | |
 | Charles E. Larard, Henry A. Golding - Engineering - 1909 - 508 pages
...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... | |
 | Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 296 pages
...power of a number is n times the logarithm of the number. (б) The logarithm of the real positive nth root of a number is the logarithm of the number divided by n. EXERCISES Express the logarithms of the following expressions in terms of the logarithms of integers... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Logarithms - 1909 - 264 pages
...(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,... | |
 | Levi Leonard Conant - Plane trigonometry - 1909 - 290 pages
...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... | |
 | Stimson Joseph Brown, Paul Capron - Algebra - 1910 - 212 pages
...(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,... | |
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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. 
