Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

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?

share|improve this question
add comment

2 Answers

up vote 9 down vote accepted
Maximize[{Log[n]^(1/Log[n]), n > 1}, n]

(* {E^(1/E), {n -> E^E}} *)
share|improve this answer
    
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
add comment

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.

share|improve this answer
    
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
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.