 ... the logarithm of any power of a quantity is equal to the logarithm of the quantity multiplied by the exponent of the power. Assume the equation a  Plane Trigonometry - Page 56by Webster Wells - 1887 - 103 pagesFull view - About this book
 | Henry W. Jeans - Trigonometry - 1842 - 138 pages
...10 log. a : ifx = a?b3 then log. x = 2 log. a +3 log. b. 1 22 (d) The logarithm of the root of any quantity is equal to the logarithm of the quantity divided by the number denoting the root to be extracted : thus if x = \/a or a*, log. a I then log. x = or r, log.... | |
 | John Bonnycastle - 1848 - 334 pages
...of the power. Let a" — P ; then x — log.p, and a3" = p" ; therefore log.p3 = nx = n log,P. (4) The logarithm of any root of a quantity is equal to the logarithm of the quantity dicided by the index of the root, xi Let if = p, then x = log.p and a•-= P"-; therefore Î- x 1 Hence... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...product of the logarithm of the number by the index of the power.—4th. The logarithm of the root of any quantity is equal to the logarithm of the quantity divided by the index of the root. SECTION V. See Playfair's Euclid, Supplement, Book i. Propositions 5 and 9; also Tate's Geometry, Theorems... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...er* = N, then x = log„ N, and a"' = N" ; therefore log N" = nx = n log„ N . 4. The logarithm of a root of a quantity is equal to the logarithm of the quantity divided by the index of the root. XI Let (f = N, then x = Iog0 N, and a" = N" ; therefore ix 1 loe N* = - = — Ioc0 N. nn 5. The logarithms... | |
 | Henry William Jeans - 1858 - 106 pages
...log. a;= 10 log. a If x=a№, then log. a; =2 log. a+3 log. 6 (a7) The logarithm of the root of any quantity is equal to the logarithm of the quantity divided by the number denoting the root to be extracted : thus, if x=-^/a, or x=a$, then loar, a , log. x=-S— or... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...quanttty, is equal to the product of the logarithm of the quantity by the exponent of the power, 4. The logarithm of any root of a quantity, is equal to the logarithm of thequantity, divided by the index of the root. These lour principles arc used for abbreviating the... | |
 | James Pryde - Navigation - 1867 - 506 pages
...cubes of 52-38; 9-3425; 6-5125; and -08475. (91.) n fourth power of 3-1416; 01-5236; and 53-175. 68. The logarithm of any root of a quantity is equal to the logarithm of the quantitv divided by the index or exponent of ths root. x , Let cf = P, then x = log. 0P, and an = P"... | |
 | Henry William Jeans - 1873 - 292 pages
...log. a;=ЛО log. a. Iîx=a?ba, then log. x=2 log. a + 3 log. b. (d) The logarithm of the root of any quantity is equal to the logarithm of the quantity divided by the number denoting the root to be extracted : Thus, if x= v^a=ai, then log. x= — ^ — or ^ log. а... | |
 | Carl Bremiker - Logarithms - 1875 - 544 pages
...to the product of the logarithm of the quantity and the exponent of the power. The logarithm of the root of a quantity is equal to the logarithm of the quantity divided by the index of the root. These four principles embrace the use of logarithms; by which we may easily find for any given number... | |
 | Frederick Augustus Porter Barnard - Encyclopedias and dictionaries - 1877 - 916 pages
...quantity is equal to the logarithm uf the quantity multiplied by the exponent of the pow«-r; ami 4th, the logarithm of any root of a quantity is equal to...logarithm of the quantity divided by the index of tho root. In npplying these principles the logarithms needed aro taken from tables called tables of... | |
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