| John Charles Stone, James Franklin Millis - Algebra - 1911 - 311 pages
...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 - Algebra - 1912 - 238 pages
...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... | |
| Frederick Howland Somerville - Algebra - 1913 - 458 pages
...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.... | |
| Robert Édouard Moritz - Trigonometry - 1913 - 560 pages
...is to be extracted, -is the logarithm of the resulting root; hence, n The logarithm of any root of a **number is equal to the 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.... | |
| George Wentworth, David Eugene Smith - Algebra - 1913 - 458 pages
...=,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... | |
| George Albert Wentworth - 1913 - 296 pages
...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 - Plane trigonometry - 1914 - 338 pages
...= p log A . For example, log 7.26 = 5 log 7.2. 7. 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 root.** For if x = \ogA, then A = 10*. 1 ЯС Taking the rth root, AT = 10?. ., . .- x \osA Hence log.Ar =... | |
| Henry Charles Wolff - Mathematics - 1914 - 332 pages
...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... | |
| George Wentworth, David Eugene Smith - Plane trigonometry - 1914 - 348 pages
...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... | |
| Claude Irwin Palmer, Charles Wilbur Leigh - Plane trigonometry - 1914 - 308 pages
...number multiplied by the exponent of the power. By (c) . (7) The logarithm of a root of a number equals **the logarithm of the number divided by the index of the root.** By (d). 1 The truth of the statements in Art. 1 follows from these theorems. That is, the process of... | |
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