Use mathematical induction to prove that n lnn for all inte

Use mathematical induction to prove that n > ln(n) for all integers x greaterthanorequalto 1. Your proof must be submitted to the instructor on a paper copy. Your proof must You may use: any of the properties of logarithms from Section 4.3. the fact that y = ln(x) is an increasing function, that is if a

Solution

Domain of ln(x) is (0 , infinity ) , because log is defined on positive numbers only.

Since its derivative 1/x is positive over (0, infinity ) , therefore it’s increasing. Every increasing function

on an interval is one-to-one and always increasing.

Hence for a<b => ln(a) < ln(b) is always true.