Why does n^(ln (ln n)) = ln n^(ln n) ?



Answered question


Why does n ln ln n = ( ln n ) ln n ?
Note: this is (part of my solution to) a homework question. Please DO NOT tell me the answer!
I am trying to compare the following functions:
n ln ln n ( ln n ) ln n
It appears that they are equal (assuming n > 1), but I have absolutely no idea why this would be the case.
I am missing something really obvious and I have been hitting my head on this for about 45 minutes. A hint would be appreciated.

Answer & Explanation

Lamar Esparza

Lamar Esparza

Beginner2022-09-07Added 8 answers

Try put the two expressions into the form e ( ) and compare.
Formula : x y = e y ln ( x )
Bruce Sherman

Bruce Sherman

Beginner2022-09-08Added 2 answers

Take the logarithm of both expressions.
ln ( x y ) = y ln ( x ) ln ( ln ( n ) ) ln ( n ) = ln ( n ) ln ( ln ( n ) )

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