化简：（log2(3)+log4(9)+log8(27)+…+log2n(3^n))*log2(8的n次方根)
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A=m^k,B=n^k,则logA(B)=logm(n)
8^(1/n)=(2*2*2)^(1/n)=2^(3/n),故 log2(8^(1/n))=3/n
所以 log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n)=n*log2(3)
所以 (log2(3)+log4(9)+log8(27)+…+log(2^n)(3^n))*log2(8^(1/n))=3*log2(3)