 The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.  Plane Trigonometry - Page 42by Elmer Adelbert Lyman, Edwin Charles Goddard - 1899 - 91 pagesFull view - About this book
 | John Charles Stone - Business mathematics - 1908 - 266 pages
...n. Then, 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 0... | |
 | William Findlay Shunk - Railroad engineering - 1908 - 386 pages
...the number multiplied by the exponent of the power. The logarithm of any root of a number is equal to the logarithm of the number divided by the index of the root. . 6. The preceding principles enable us to abridge labor in arithmetical calculations, by using simple... | |
 | 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... | |
 | 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,... | |
 | 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... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 216 pages
...logarithm of the dividend minня the logarithm of the divisor. (b) Tlie logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log Y = log a — log b and log л/о = Y D n EXERCISES By means of logarithms approximate... | |
 | 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, logaí/ñ... | |
 | 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« A/M.... | |
 | 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... | |
 | 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... | |
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