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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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2 Answers 2

up vote 10 down vote accepted
Maximize[{Log[n]^(1/Log[n]), n > 1}, n]

(* {E^(1/E), {n -> E^E}} *)
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Log[1] is ... mmmm ... –  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
4  
$e^{\mathrm{mmmm}}-1=0$: belisarius' identity. –  rm -rf 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

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