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Sage Garrison

Sage Garrison

Answered question

2022-06-03

Proof of e ln ( x ) ln ( 2 ) , which natural logarithm do I bring down?
I'm currently stumped with the proof for the following problem:
F ( x ) = 2 ln ( x )
F ( x ) = y
y = 2 ln ( x )
ln ( y ) = ln ( 2 ln ( x ) )
ln ( y ) = ln ( x ) ln ( 2 )
y = e ln ( x ) ln ( 2 )
Now, how do I know which natural logarithm to bring down? What ensures that my answer must be 2 ln ( x ) instead of x ln ( 2 ) ?
Thanks! :)

Answer & Explanation

Posavkah6qnsz

Posavkah6qnsz

Beginner2022-06-04Added 3 answers

Both are the same:
2 log ( x ) = e log ( x ) log ( 2 ) = x log ( 2 )

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