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## Homework Statement

Compute Limit as x--> infinity of (logx)

^{(log(logx))}/ x

## The Attempt at a Solution

Graphically, I see that the answer is perhaps zero, but I am not sure how to approach this algebraically. I worked at this for a couple hours, trying L'Hospital's rule but that did not really lead me anywhere. Is there some tricky substitution I am missing?

Can I do this?

Rewrite (logx)

^{log(log(x))}

as

10

^{(log(logx))2}

and then x as

10

^{logx}

and evaluate the limit of the exponents? (as in as a ratio)?

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