How to simplify this? \(\displaystyle{\frac{{{n}^{{{\log{{m}}}}}}}{{{m}^{{{\log{{n}}}}}}}}\)

Ekwadorkadba3

Ekwadorkadba3

Answered question

2022-04-08

How to simplify this?
nlogmmlogn

Answer & Explanation

madking711kzcb

madking711kzcb

Beginner2022-04-09Added 9 answers

Hint: Apply log to the whole thing and use the quotient and powers rules for log. You should get a very simple result, which you can exponentiate to find your answer.
Terzago66cl

Terzago66cl

Beginner2022-04-10Added 8 answers

First note that x=alogax
So we find that nlogm=elog(nlogm)=elogmlogn
Similarly, we find that mlogn=elog(mlogn)=elognlogm

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