SOLUTION: find m, 9^4^m = 4^9^m

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Question 1209564: find m,
9^4^m = 4^9^m
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
   

 

Take natural logs of both sides:

 

4%5Em%2Aln%289%29%22%22=%22%229%5Em%2Aln%284%29

4%5Em%2F9%5Em%22%22=%22%22ln%284%29%2Fln%289%29

%284%2F9%29%5Em%22%22=%22%22ln%284%29%2Fln%289%29

Take natural logs of both sides:

ln%28%284%2F9%29%5Em%29%22%22=%22%22ln%28ln%284%29%2Fln%289%29%29

m%2Aln%284%2F9%29%22%22=%22%22ln%28ln%284%29%2Fln%289%29%29

m%2A%28ln%284%29-ln%289%29%5E%22%22%29%22%22=%22%22ln%28ln%284%29%5E%22%22%29-ln%28ln%289%29%5E%22%22%29

m%22%22=%22%22

approximately 0.567941284.

Edwin