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

miniliv4

miniliv4

Answered question

2022-09-06

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 ) )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?