...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....

...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...

...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...

...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...

...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...

...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...

...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"...

...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...

...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...

...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...