2.(log23+log49+log827+…+log2n3n)× log9n√32这倒怎么算啊.

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2.(log23+log49+log827+…+log2n3n)× log9n√32这倒怎么算啊.
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2.(log23+log49+log827+…+log2n3n)× log9n√32这倒怎么算啊.
2.(log23+log49+log827+…+log2n3n)× log9n√32
这倒怎么算啊.

2.(log23+log49+log827+…+log2n3n)× log9n√32这倒怎么算啊.
log4 9=log(2^2) (3^2)=log2 3
...
同理log(2^n)(3^n)=log2 3
所以,原式=(log2 3+log2 3+...+log2 3)*log(3^(2n) 2^(5/2)
=[nlog2 3]*(5/2)/2n*log3 2
=n*5/(4n)
=5/4