Can someone explain why x^(log(a)) = a^(log(x))?

ajanlr

ajanlr

Answered question

2022-10-25

Can someone explain why x log ( a ) = a log ( x ) ?

Answer & Explanation

Momellaxi

Momellaxi

Beginner2022-10-26Added 14 answers

x log ( a ) = ( e log ( x ) ) log ( a ) = e log ( x ) log ( a ) = a log ( x )
This only works if x and a are both positive real numbers.
Marlene Brooks

Marlene Brooks

Beginner2022-10-27Added 3 answers

take the log for both sides to get
log ( x l o g ( a ) ) = log ( a log ( x ) )
log ( a ) l o g ( x ) = log ( a ) log ( x )
It is clear that the a, x should be positive

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