(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)=

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(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)=
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(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)=
(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)=

(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)=
log2^n(3^n)=log2(3)
log2(3)+log4(9)+……+log2^n(3^n)=nlog2(3)
log9(n次根号8)=1/nlog9(8)=1/n*3/2*log3(2)
(log2(3)+log4(9)+……+log2^n(3^n))·log9(n次根号8)
=nlog2(3)*1/n*3/2*log3(2)
=3/2