Show that x b is oa for any a b R with a 1 small ohSolution

Show that x^ b is o(a) for any a, b R with a > 1. (small oh)

Solution

Order of element of a group :

Order of element a is defined as n is any least positive integer such that a^n =e.

(e = identity element).

n is order of the element.

order of element a is denoted by o(a).

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In the given problem,

actually x = a.

Hence,

Order of element a is defined as b is any least positive integer such that a^b =e.

(e = identity element).

b is order of the element.

order of element a is denoted by o(a).