Is it correct? n^(log x)=x^(log n) Can you proof and describe that, for any base? Please explain completely. Thank you.

shadyufog0

shadyufog0

Answered question

2022-09-29

Is it correct? n ( log x ) = x ( log n ) ?
Can you proof and describe that, for any base? Please explain completely. Thank you.

Answer & Explanation

Danielle Gilbert

Danielle Gilbert

Beginner2022-09-30Added 5 answers

n ( log x ) = ( e log n ) ( log x ) = e ( log n ) ( log x ) = e ( log x ) ( log n ) = ( e log x ) ( log n ) = x ( log n )
If you use log to a different base b, then use b instead of e
rialsv

rialsv

Beginner2022-10-01Added 3 answers

Hint: compute the logarithm of both sides. Since the logarithm function is one-to-one this will tell you if they are equal.

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