# How to Maximize[Log[n]^(1/Log[n]), n]

I am new to Mathematica and am trying to work out how to use Maximize.

Maximize[Log[n]^(1/Log[n]),n]


Should give a solution at $e^e$. However in Mathematica you don't get anything. What's the right way to do this?

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Maximize[{Log[n]^(1/Log[n]), n > 1}, n]

(* {E^(1/E), {n -> E^E}} *)

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Log[1] is ... mmmm ... – Dr. belisarius Nov 8 '13 at 18:31
Oh, you think it gives up without n>1 because it doesn't know what to do with complex expressions? – ssch Nov 8 '13 at 18:33
$e^{\mathrm{mmmm}}-1=0$: belisarius' identity. – R. M. Nov 8 '13 at 18:35
Thank you. Limit[Log[x]^(1/Log[x]), x->1] is $0$ . – felix Nov 9 '13 at 8:53

You could use Solve to find where the derivative is 0:

Solve[D[Log[n]^(1/Log[n]), n] == 0, n]
(* {{n -> E^E}} *)


I find it strange that Maximize doesn't realize this.

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Thank you. That was how I did it in the end. I was just trying to work out how to use Maximize for when I can't find the solution so easily. – felix Nov 8 '13 at 18:19