 | Isaac Dalby - Mathematics - 1806 - 526 pages
...161, 187, thus; Since /xr*—1 = /, therefore r"~~l = -f : and because the logarithm of any power of a number is equal to the logarithm of that number multiplied by the index or exponent denoting the power (187 Arith.) therefore (72 — l) log. r = log. -., that is, n R —... | |
 | Encyclopedias and dictionaries - 1816 - 746 pages
...fince n may be either a whole number, or a fraction, it follows, that the logarithm of any power of a number is equal to the logarithm of that number, multiplied by the exponent of the power ; alfo, that the logarithm of any root of a number is equal to the logarithm... | |
 | Bézout - Arithmetic - 1825 - 258 pages
...numbers is equal to the logarithm of their product, number 227. 92. The logarithm of any power of a number is equal to the logarithm of that number, multiplied by the index of the power, number 228. 93. The logarithm of the root of a number is equal to the logarithm of this... | |
 | Thomas Curtis (of Grove house sch, Islington) - 412 pages
...since n may be either a whole number or a fraction, it follows, that the logarithm of any power of a number is equal to the logarithm of that number, multiplied by the exponent of the power ; also, that the logarithm of any root of a number is equal to the logarithm... | |
 | Charles Davies - Surveying - 1830 - 390 pages
...logarithm of their quotient. 6. If in the equation az=n, both members be raised to the mth power, a™z=nm. Here, mx is the logarithm of nm ; from which it appears,...the index of that power. 7. If the mth root of both members of the equation az=n, x be taken, then, a'"=nm ; but - is the logarithm of nm ; from which... | |
 | Charles Davies - Surveying - 1830 - 318 pages
...logarithm of nm ; from which it appears, that tht logarithm of the power of any number, in equal lo the logarithm of that number, multiplied by the index of that power. 7. If tho mth root of both members of the equation ax=n, ."' 'ix .1 be taken, then, o"=n"1; but - is the... | |
 | Robert Gibson - Surveying - 1833 - 436 pages
...conclude, that the differin 6. If in the equation a*=n, both members be raised to the »ith power, amx = nm. Here, mx is the logarithm of nm ; from which it...number, multiplied by the index of that power. 7. If the with root of both members of the equation ax=n, x- I x 1 be taken, then, am=nm; but- is the logarithm... | |
 | William Chauvenet - Binomial theorem - 1843 - 102 pages
...found in the table to be the logarithm of the required quotient. 62. The logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. For b being any number, we have a'°g-4=6. But a'°s-*''=5'', whence the equation... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...log. 2000 = x + 3, log. 2000000 =, &c. We have seen, in Art. 324, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, log. 4 = 2a;, log. 32 = log. 8 = 3x, log. 64 = log. 16 = 4a;, log. 128... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...log. 2000 = x + 3, log. 2000000 =, &c. We have seen, in Art. 324, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, log. 4 = 2ar, log. 32 = Hence we find, also, that log. 40 = Zx+ 1, log.... | |
| |
Art. 340, that the logarithm of any power of a number is equal to the logarithm of that number multiplied by the exponent of the power. Hence, to involve a number by logarithms, we have the following RULE. 
