One inequality with two variables

 One inequality with two variables

I would just like to know if this:

((a - b)/(b*Log[b])) - Log[Log[a]] + Log[Log[b]]

exceeds 0 for any combination of a and b, being both variables positive integers.

I have tried to compute it on Mathematica but I only get hundreds of errors.

What would be the way to know if there is a solution to

((a - b)/(b*Log[b])) - Log[Log[a]] + Log[Log[b]]<0

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