calculus inequality: (x - 1)^2 >= x ln^2(x)

[BrainMan]

Assume that x is a positive real number.

Prove the following inequality:

(x-1)^2 is greater than or equal to x[(ln(x))^2].

I'm not really sure how to do this. Any help you can offer would be greatly appreciated.

 

[tkhunny]

It's not coming to me right away.

It may be beneficial to separate and prove two pieces, x < 1 and x > 1. Then there would be some Intermediate Value ideas.