Question

How to show that x > (ln x)^3 ? How to show that x > (ln x)^3 ? @Mathematics

Answer 1

Considering values of x in [2, infinity)

Answer 2

Counter-example:

10 > (ln(10))^3
10 > (2.302585...)^3
10 > 12.20807...
Not true.

Answer 3

This is weird since my book says. Since n > (ln n)^3 for large n, The sum (1/(ln n)^3) diverges since the sums (1/n) diverges ._.

Answer 4

This is weird since my book says. Since n > (ln n)^3 for large n, The sum (1/(ln n)^3) diverges since the sums (1/n) diverges ._.

Answer 5

by the direct comparison test

Answer 6

Well, once your values do get rather big this should hold... but it doesn't hold from 2 to infinity.