Solving equation \(\displaystyle{{\log}_{{y}}{\left({{\log}_{{y}}{\left({x}\right)}}\right)}}={{\log}_{{n}}{\left({x}\right)}}\) for n I'm just wondering,

Aleah Choi

Aleah Choi

Answered question

2022-04-03

Solving equation logy(logy(x))=logn(x) for n
I'm just wondering, if I log a constant twice with the same base y,
logy(logy(x))=logn(x)
Can it be equivalent to logging the same constant with base n? If yes, what is variable n equivalent to?

Answer & Explanation

davane6a7a

davane6a7a

Beginner2022-04-04Added 8 answers

logy(logy(x))=logn(x)
logy(logy(x))=loge(x)loge(n)
loge(n)=loge(x)logy(logy(x))
n=eloge(x)logy(logy(x))
Thus, for given x,y, if eloge(x)logy(logy(x)) is defined, then that is the value for n.

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