 | John Charles Stone, James Franklin Millis - 1911 - 698 páginas
...Then n? = (a1)»1 = afx. Hence, Iog0 if = px=p loga n. IV. The logarithm of a root of a number equals the logarithm of the number, divided by the index of the root. That is, rr log« я lOga V« = p For, let a1 = n. X Then -Ñ/ñ = vV = a'. By use of the above principles... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - 1912 - 238 páginas
...logarithm of the dividend minus the logarithm of the divisor. (Ь) The logarithm of a root of a number is the logarithm of the number divided by the index of the root. That is log - = log a — log b and log \/a = Ь п EXERCISES By means of logarithms approximate the... | |
 | Robert Édouard Moritz - 1913 - 562 páginas
...the quantity whose яth root is to be extracted, -is the logarithm of the resulting root; hence, n The logarithm of any root of a number is equal to...logarithm of the number divided by the index of the root to be extracted, or if p=4W, iog/» = !^r. я Thus log Viy = i log 17. 26. Logarithms of Special Values.... | |
 | Frederick Howland Somerville - 1913 - 458 páginas
...log m' = px. But, from (1), x = log m, (Art. 438) Hence, log m" = pQog n8). 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. (I) Raising both members to the power indicated by-, 109=n89. l Whence, log m9 = -. (Art.... | |
 | 1912 - 1052 páginas
...raised to a power is equal to the power times the logarithm of the number, and the logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. 3. Since a° = I, then loga i = o The logarithm of unity is zero. Since a1 = a, then log. a = i. The... | |
 | George Albert Wentworth - 1913 - 296 páginas
...That is, 10g2 322 = 2 log2 32. 235. Logarithm of a Root. The logarithm of a root of a number equals the logarithm of the number divided by the index of the root. If ж = log .4, then Л =10*. IX Taking the rth root, Aг = 10r. \ 1 x Hence log Ar = As in § 234,... | |
 | George Wentworth, David Eugene Smith - 1913 - 478 páginas
...=,10^*. Hence log Af = px = p log A. 321. Logarithm of a Root. The logarithm of a root of a number equals the logarithm of the number divided by the index of the root. If x = log A , then A = 10«. i Taking the г-th root, A~r = W. 1 x Hence log Ar — r r Therefore... | |
 | Henry Charles Wolff - 1914 - 332 páginas
...the power of a number is equal to the logarithm of the number multiplied by the index of the power. root of a number is equal to the logarithm of the number divided by the index of the root. ILLUSTRATION : If log 2 = 0.3010, log 4 = 2 log 2 = 2 X 0.3010 = 0.6020, and log \/2 = J log 2 = JX... | |
 | Charles Ezra Sprague - 1914 - 380 páginas
...stated, and it will be observed that it is the converse of the third rule. Rule 4: The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root. As an illustration, let it be required to find the square root of 49. 49 nl 1.6902 V49~, or 49* nl... | |
 | George Wentworth, David Eugene Smith - 1914 - 348 páginas
...1024 = 2-5 = 2 log, 32. That is, Iog2 322 = 2 Iog2 32. 43. Logarithm of a Root. The logarithm of a root of a number is equal to the logarithm of the number divided by the index of the rout. Por if A = 10*, 1 X taking the rth root, A 7' = KK ix Hence loeAr = r — log Л r The propositions... | |
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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. 
